{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# PyZeta Teaser" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This *teaser* notebook shows some of the very basic functionality of **PyZeta** in terms of the\n", "scripting API. No real effort was made to follow best practices with respect to **PyZeta**-based\n", "applications in order to arrive at some interesting plots as fast as possible.\n", "\n", "The goal here is to wet your appetit to start your own resonance adventure!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Imports" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First some basic imports are needed - some of these would be abstracted away when programming\n", "with the highest-level enduser API." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from typing import Final\n", "from colorsys import hls_to_rgb\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from pyzeal.rootfinders.rootfinder import RootFinder\n", "from pyzeal.pyzeal_types.algorithm_types import AlgorithmTypes\n", "from pyzeal.pyzeal_types.estimator_types import EstimatorTypes\n", "from pyzeal.settings.json_settings_service import JSONSettingsService\n", "\n", "from pyzeta.core.pyzeta_types.function_systems import FunctionSystemType\n", "from pyzeta.core.pyzeta_types.map_systems import MapSystemType\n", "\n", "from pyzeta.framework.initialization.initialization_handler import (\n", " PyZetaInitializationHandler,\n", ")\n", "from pyzeta.core.zetas.selberg_zeta import SelbergZeta\n", "from pyzeta.core.pyzeta_types.integrals import OrbitIntegralType\n", "from pyzeta.core.zetas.wzeta import WeightedZeta\n", "from pyzeta.core.distributions.ruelle_distribution import RuelleDistribution\n", "\n", "PyZetaInitializationHandler.initPyZetaServices()\n", "# deactivate PyZEAL progress bar\n", "JSONSettingsService().verbose = False\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hyperbolic Cylinder Resonances" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We begin by calculating some quantum resonances for the Schottky and flow adapted hyperbolic\n", "cylinders. These resonances are theoretically known to be located at\n", "\\begin{equation}\n", "-\\mathbb{N}_0 + \\frac{2\\pi\\mathrm{i}}{\\ell} \\mathbb{Z}\n", "\\end{equation}\n", "for $\\ell$ the width of the closed geodesic around the cylinder waist. Their respective multiplicities\n", "are always $2$. Both representations should of course yield these values!" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "resonance=1.885j --> order=2\n", "resonance=-0j --> order=2\n", "resonance=0.628j --> order=2\n", "resonance=1.256j --> order=2\n", "resonance=1.885j --> order=2\n", "resonance=-0j --> order=2\n", "resonance=0.628j --> order=2\n", "resonance=1.256j --> order=2\n" ] }, { "data": { "image/png": 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f//mfmjFjxkVrFi9erDfeeEN79uwJ9s2aNUv19fUqLS2VJLlcLt188816/vnnJUktLS1yOp26//77tWTJkq+ch9/vl91ul8/nU0JCwpUeDgAA6EThvH93+DUsFRUVcrvdIX1ZWVmqqKiQJDU1NamysjKkJioqSm63O1jzZY2NjfL7/SENAABErg4PLB6PR8nJySF9ycnJ8vv9+uyzz3T69Gk1Nze3W+PxeNods6ioSHa7PdicTmeHzR8AAHS9bnmXUEFBgXw+X7BVV1d39ZQAAEAH6tXRP8DhcMjr9Yb0eb1eJSQkqHfv3oqOjlZ0dHS7NQ6Ho90xY2NjFRsb22FzBgAAZunwMyyZmZkqKysL6Xv33XeVmZkpSYqJidG4ceNCalpaWlRWVhasAQAAPVvYgaWhoUFVVVWqqqqS1HrbclVVlY4fPy6p9eOaOXPmBOvvu+8+HT58WI888oj279+vX//619qwYYN+8pOfBGvy8/P1wgsvaM2aNdq3b58WLVqkQCCgvLy8r3l4AAAgEoT9kdDOnTs1efLk4Ov8/HxJ0ty5c1VSUqLa2tpgeJGkYcOG6Y033tBPfvITrVixQoMHD9bvfvc7ZWVlBWtmzpypU6dOaenSpfJ4PMrIyFBpaWmbC3EBAEDP9LWew2IKnsMCAED3Y9RzWAAAAL4uAgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMN4VBZbi4mKlpaUpLi5OLpdLO3bsuGjtpEmTZLPZ2rSpU6cGa+bNm9dme3Z29pVMDQAARKBe4e6wfv165efna+XKlXK5XFq+fLmysrJ04MABJSUltal/7bXX1NTUFHx95swZpaen63vf+15IXXZ2tv793/89+Do2NjbcqQEAgAgV9hmW5557TgsWLFBeXp5uvPFGrVy5Un369NHq1avbre/fv78cDkewvfvuu+rTp0+bwBIbGxtS169fvys7IgAAEHHCCixNTU2qrKyU2+2+MEBUlNxutyoqKi5rjFWrVmnWrFmKj48P6S8vL1dSUpJGjhypRYsW6cyZMxcdo7GxUX6/P6QBAIDIFVZgOX36tJqbm5WcnBzSn5ycLI/H85X779ixQ3v27NG9994b0p+dna21a9eqrKxMTz31lDZt2qScnBw1Nze3O05RUZHsdnuwOZ3OcA4DAAB0M2Ffw/J1rFq1SmPGjNGECRNC+mfNmhX8+5gxYzR27Fhdd911Ki8v1x133NFmnIKCAuXn5wdf+/1+QgsAABEsrDMsAwYMUHR0tLxeb0i/1+uVw+G45L6BQEDr1q3T/Pnzv/LnDB8+XAMGDNChQ4fa3R4bG6uEhISQBgAAIldYgSUmJkbjxo1TWVlZsK+lpUVlZWXKzMy85L6vvPKKGhsbdc8993zlz6mpqdGZM2eUkpISzvQAAECECvsuofz8fL3wwgtas2aN9u3bp0WLFikQCCgvL0+SNGfOHBUUFLTZb9WqVZoxY4a+8Y1vhPQ3NDTo4Ycf1rZt23T06FGVlZVp+vTpGjFihLKysq7wsAAAQCQJ+xqWmTNn6tSpU1q6dKk8Ho8yMjJUWloavBD3+PHjiooKzUEHDhzQli1b9M4777QZLzo6Wh999JHWrFmj+vp6paam6s4779QTTzzBs1gAAIAkyWZZltXVk/i6/H6/7Ha7fD4f17MAANBNhPP+zXcJAQAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAzOPzSTU17W+rqWndDqBHIbAAMIvPJ2VnSxMnKnD4gGzLbLItsynQFJCqq6WJE1u3E1qAHoXAAsAsZ89KdXXS4cNSTvaF/poaadKk1v66utY6AD0GgQWAWQYPVuDdNxW4IU2BE0eD3YFpWQpUH1bghjSpvFwaPLirZgigC/Tq6gkAwJdd++Io6fuhfcl3H/vr347Kcjo7fU4AuhZnWAAAgPEILACM01DQoIbZ++XdMDTY531GangpTQ2z93fhzAB0FQILAOPEez9R/JS7FH/w2IW+QWmK/8tRxU+5q/VuIQA9CoEFgFm+eDfQsLQL/W+VSsOHt/ZPmnTx57QAiEhcdAvALH37SklJkqT498pDL7AtL28NK0lJrXUAegwCCwCz2O1SaWnrc1a+fOuy0ylt2tQaVuz2rpkfgC5BYAFgHrv94oGE568APRLXsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeFcUWIqLi5WWlqa4uDi5XC7t2LHjorUlJSWy2WwhLS4uLqTGsiwtXbpUKSkp6t27t9xutw4ePHglUwMAABEo7MCyfv165efnq7CwULt27VJ6erqysrJUV1d30X0SEhJUW1sbbMeOHQvZ/vTTT+uXv/ylVq5cqe3btys+Pl5ZWVk6d+5c+EcEAAAiTtiB5bnnntOCBQuUl5enG2+8UStXrlSfPn20evXqi+5js9nkcDiCLTk5ObjNsiwtX75cjz76qKZPn66xY8dq7dq1OnnypDZu3HhFBwUAACJLWIGlqalJlZWVcrvdFwaIipLb7VZFRcVF92toaNDQoUPldDo1ffp0/fnPfw5uO3LkiDweT8iYdrtdLpfromM2NjbK7/eHNAAAELnCCiynT59Wc3NzyBkSSUpOTpbH42l3n5EjR2r16tV6/fXX9R//8R9qaWnRrbfeqpqaGkkK7hfOmEVFRbLb7cHmdDrDOQwAANDNdPhdQpmZmZozZ44yMjI0ceJEvfbaaxo4cKD+7d/+7YrHLCgokM/nC7bq6uqrOGMAAGCasALLgAEDFB0dLa/XG9Lv9XrlcDgua4xrrrlGN910kw4dOiRJwf3CGTM2NlYJCQkhDQAARK6wAktMTIzGjRunsrKyYF9LS4vKysqUmZl5WWM0Nzdr9+7dSklJkSQNGzZMDocjZEy/36/t27df9pgAACCy9Qp3h/z8fM2dO1fjx4/XhAkTtHz5cgUCAeXl5UmS5syZo0GDBqmoqEiS9LOf/Uy33HKLRowYofr6ej3zzDM6duyY7r33XkmtdxA98MAD+vnPf67rr79ew4YN02OPPabU1FTNmDHj6h0pAADotsIOLDNnztSpU6e0dOlSeTweZWRkqLS0NHjR7PHjxxUVdeHEzaeffqoFCxbI4/GoX79+GjdunLZu3aobb7wxWPPII48oEAho4cKFqq+v12233abS0tI2D5gDAAA9k82yLKurJ/F1+f1+2e12+Xw+rmcBAKCbCOf9m+8SAgAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjXVFgKS4uVlpamuLi4uRyubRjx46L1r7wwgu6/fbb1a9fP/Xr109ut7tN/bx582Sz2UJadnb2lUwNAABEoLADy/r165Wfn6/CwkLt2rVL6enpysrKUl1dXbv15eXlys3N1QcffKCKigo5nU7deeedOnHiREhddna2amtrg+3ll1++siMCAAARx2ZZlhXODi6XSzfffLOef/55SVJLS4ucTqfuv/9+LVmy5Cv3b25uVr9+/fT8889rzpw5klrPsNTX12vjxo3hH4Ekv98vu90un8+nhISEKxoDAAB0rnDev8M6w9LU1KTKykq53e4LA0RFye12q6Ki4rLG+N///V99/vnn6t+/f0h/eXm5kpKSNHLkSC1atEhnzpy56BiNjY3y+/0hDQAARK6wAsvp06fV3Nys5OTkkP7k5GR5PJ7LGmPx4sVKTU0NCT3Z2dlau3atysrK9NRTT2nTpk3KyclRc3Nzu2MUFRXJbrcHm9PpDOcwAABAN9OrM3/Yk08+qXXr1qm8vFxxcXHB/lmzZgX/PmbMGI0dO1bXXXedysvLdccdd7QZp6CgQPn5+cHXfr+f0AIAQAQL6wzLgAEDFB0dLa/XG9Lv9XrlcDguue+zzz6rJ598Uu+8847Gjh17ydrhw4drwIABOnToULvbY2NjlZCQENIAAEDkCiuwxMTEaNy4cSorKwv2tbS0qKysTJmZmRfd7+mnn9YTTzyh0tJSjR8//it/Tk1Njc6cOaOUlJRwpgcAACJU2Lc15+fn64UXXtCaNWu0b98+LVq0SIFAQHl5eZKkOXPmqKCgIFj/1FNP6bHHHtPq1auVlpYmj8cjj8ejhoYGSVJDQ4Mefvhhbdu2TUePHlVZWZmmT5+uESNGKCsr6yodJgAA6M7CvoZl5syZOnXqlJYuXSqPx6OMjAyVlpYGL8Q9fvy4oqIu5KDf/OY3ampq0t/93d+FjFNYWKjHH39c0dHR+uijj7RmzRrV19crNTVVd955p5544gnFxsZ+zcMDAACRIOznsJiI57AAAND9dNhzWAAAALoCgQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwAAMB6BBQAAGI/AAgAAjEdgAQAAxiOwAAAA4xFYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIxHYAEAAMYjsAAAAOMRWAAAgPEILAAAwHgEFgAAYDwCCwDz+HxSTU3722pqWrcD6FGuKLAUFxcrLS1NcXFxcrlc2rFjxyXrX3nlFY0aNUpxcXEaM2aM3nzzzZDtlmVp6dKlSklJUe/eveV2u3Xw4MErmRqA7s7nk7KzpYkTFTh8QLZlNtmW2RRoCkjV1dLEia3bCS1AjxJ2YFm/fr3y8/NVWFioXbt2KT09XVlZWaqrq2u3fuvWrcrNzdX8+fP1xz/+UTNmzNCMGTO0Z8+eYM3TTz+tX/7yl1q5cqW2b9+u+Ph4ZWVl6dy5c1d+ZAC6p7Nnpbo66fBhKSf7Qn9NjTRpUmt/XV1rHYAew2ZZlhXODi6XSzfffLOef/55SVJLS4ucTqfuv/9+LVmypE39zJkzFQgE9N///d/BvltuuUUZGRlauXKlLMtSamqqHnzwQT300EOSJJ/Pp+TkZJWUlGjWrFlfOSe/3y+73S6fz6eEhIRwDgeAgQKHD0g52QqcOKrkh1v7vBuGKv7gMWlYmuLf2yw5nV07SQBfWzjv32GdYWlqalJlZaXcbveFAaKi5Ha7VVFR0e4+FRUVIfWSlJWVFaw/cuSIPB5PSI3dbpfL5bromI2NjfL7/SENQOS49sVRuvb7F8KKJCXffUzX/lS69vtHCStADxRWYDl9+rSam5uVnJwc0p+cnCyPx9PuPh6P55L15/8MZ8yioiLZ7fZgc/KPFwAAEa1b3iVUUFAgn88XbNXV1V09JQBXUUNBgxpm75d3w9Bgn/cZqeGlNDXM3t+FMwPQVcIKLAMGDFB0dLS8Xm9Iv9frlcPhaHcfh8Nxyfrzf4YzZmxsrBISEkIagMgR7/1E8VPuar1m5XzfoDTF/+Wo4qfc1Xq3EIAeJazAEhMTo3HjxqmsrCzY19LSorKyMmVmZra7T2ZmZki9JL377rvB+mHDhsnhcITU+P1+bd++/aJjAohgX7wbaFjahf63SqXhw1v7J026+HNaAESkXuHukJ+fr7lz52r8+PGaMGGCli9frkAgoLy8PEnSnDlzNGjQIBUVFUmS/vEf/1ETJ07Uv/7rv2rq1Klat26ddu7cqd/+9reSJJvNpgceeEA///nPdf3112vYsGF67LHHlJqaqhkzZly9IwXQPfTtKyUlSZLi3yuX9cVr1MrLW8NKUlJrHYAeI+zAMnPmTJ06dUpLly6Vx+NRRkaGSktLgxfNHj9+XFFRF07c3HrrrXrppZf06KOP6p/+6Z90/fXXa+PGjfrWt74VrHnkkUcUCAS0cOFC1dfX67bbblNpaani4uKuwiEC6Fbsdqm0tPU5K4MHh25zOqVNm1rDit3eNfMD0CXCfg6LiXgOCwAA3U+HPYcFAACgKxBYAACA8QgsAADAeAQWAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjhf1ofhOdf1iv3+/v4pkAAIDLdf59+3Ieuh8RgeXs2bOSJOcXvyQNAAB0C2fPnpX9K74fLCK+S6ilpUUnT55U3759ZbPZuno6Xc7v98vpdKq6uprvVupArHPnYJ07D2vdOVjnCyzL0tmzZ5WamhryxcntiYgzLFFRURr85W91hRISEnr8fwydgXXuHKxz52GtOwfr3Oqrzqycx0W3AADAeAQWAABgPAJLBIqNjVVhYaFiY2O7eioRjXXuHKxz52GtOwfrfGUi4qJbAAAQ2TjDAgAAjEdgAQAAxiOwAAAA4xFYAACA8Qgs3dAnn3yiH/zgB0pISFBiYqLmz5+vhoaGS+5z7tw5/ehHP9I3vvENXXvttfrbv/1beb3edmvPnDmjwYMHy2azqb6+vgOOoPvoiLX+05/+pNzcXDmdTvXu3Vvf/OY3tWLFio4+FKMUFxcrLS1NcXFxcrlc2rFjxyXrX3nlFY0aNUpxcXEaM2aM3nzzzZDtlmVp6dKlSklJUe/eveV2u3Xw4MGOPIRu4Wqu8+eff67FixdrzJgxio+PV2pqqubMmaOTJ0929GEY72r/Pn/RfffdJ5vNpuXLl1/lWXdDFrqd7OxsKz093dq2bZv1hz/8wRoxYoSVm5t7yX3uu+8+y+l0WmVlZdbOnTutW265xbr11lvbrZ0+fbqVk5NjSbI+/fTTDjiC7qMj1nrVqlXWj3/8Y6u8vNz6+OOPrRdffNHq3bu39atf/aqjD8cI69ats2JiYqzVq1dbf/7zn60FCxZYiYmJltfrbbf+ww8/tKKjo62nn37a2rt3r/Xoo49a11xzjbV79+5gzZNPPmnZ7XZr48aN1p/+9CfrO9/5jjVs2DDrs88+66zDMs7VXuf6+nrL7XZb69evt/bv329VVFRYEyZMsMaNG9eZh2Wcjvh9Pu+1116z0tPTrdTUVOsXv/hFBx+J+Qgs3czevXstSdb//M//BPveeusty2azWSdOnGh3n/r6euuaa66xXnnllWDfvn37LElWRUVFSO2vf/1ra+LEiVZZWVmPDywdvdZf9MMf/tCaPHny1Zu8wSZMmGD96Ec/Cr5ubm62UlNTraKionbr7777bmvq1KkhfS6Xy/r7v/97y7Isq6WlxXI4HNYzzzwT3F5fX2/FxsZaL7/8cgccQfdwtde5PTt27LAkWceOHbs6k+6GOmqda2pqrEGDBll79uyxhg4dSmCxLIuPhLqZiooKJSYmavz48cE+t9utqKgobd++vd19Kisr9fnnn8vtdgf7Ro0apSFDhqiioiLYt3fvXv3sZz/T2rVrv/JLqHqCjlzrL/P5fOrfv//Vm7yhmpqaVFlZGbI+UVFRcrvdF12fioqKkHpJysrKCtYfOXJEHo8npMZut8vlcl1yzSNZR6xze3w+n2w2mxITE6/KvLubjlrnlpYWzZ49Ww8//LBGjx7dMZPvhnhX6mY8Ho+SkpJC+nr16qX+/fvL4/FcdJ+YmJg2/6gkJycH92lsbFRubq6eeeYZDRkypEPm3t101Fp/2datW7V+/XotXLjwqszbZKdPn1Zzc7OSk5ND+i+1Ph6P55L15/8MZ8xI1xHr/GXnzp3T4sWLlZub22O/wK+j1vmpp55Sr1699OMf//jqT7obI7AYYsmSJbLZbJds+/fv77CfX1BQoG9+85u65557OuxnmKKr1/qL9uzZo+nTp6uwsFB33nlnp/xM4Ov6/PPPdffdd8uyLP3mN7/p6ulElMrKSq1YsUIlJSWy2WxdPR2j9OrqCaDVgw8+qHnz5l2yZvjw4XI4HKqrqwvp/7//+z998skncjgc7e7ncDjU1NSk+vr6kP/z93q9wX3ef/997d69W7///e8ltd51IUkDBgzQT3/6Uy1btuwKj8w8Xb3W5+3du1d33HGHFi5cqEcfffSKjqW7GTBggKKjo9vcodbe+pzncDguWX/+T6/Xq5SUlJCajIyMqzj77qMj1vm882Hl2LFjev/993vs2RWpY9b5D3/4g+rq6kLOdDc3N+vBBx/U8uXLdfTo0at7EN1JV19Eg/CcvxB0586dwb633377si4E/f3vfx/s279/f8iFoIcOHbJ2794dbKtXr7YkWVu3br3o1e6RrqPW2rIsa8+ePVZSUpL18MMPd9wBGGrChAnWP/zDPwRfNzc3W4MGDbrkRYrf/va3Q/oyMzPbXHT77LPPBrf7fD4uur3K62xZltXU1GTNmDHDGj16tFVXV9cxE+9mrvY6nz59OuTf4t27d1upqanW4sWLrf3793fcgXQDBJZuKDs727rpppus7du3W1u2bLGuv/76kFtta2pqrJEjR1rbt28P9t13333WkCFDrPfff9/auXOnlZmZaWVmZl70Z3zwwQc9/i4hy+qYtd69e7c1cOBA65577rFqa2uDrae8Aaxbt86KjY21SkpKrL1791oLFy60EhMTLY/HY1mWZc2ePdtasmRJsP7DDz+0evXqZT377LPWvn37rMLCwnZva05MTLRef/1166OPPrKmT5/Obc1XeZ2bmpqs73znO9bgwYOtqqqqkN/dxsbGLjlGE3TE7/OXcZdQKwJLN3TmzBkrNzfXuvbaa62EhAQrLy/POnv2bHD7kSNHLEnWBx98EOz77LPPrB/+8IdWv379rD59+ljf/e53rdra2ov+DAJLq45Y68LCQktSmzZ06NBOPLKu9atf/coaMmSIFRMTY02YMMHatm1bcNvEiROtuXPnhtRv2LDBuuGGG6yYmBhr9OjR1htvvBGyvaWlxXrssces5ORkKzY21rrjjjusAwcOdMahGO1qrvP53/X22hd//3uiq/37/GUEllY2y/rrxQoAAACG4i4hAABgPAILAAAwHoEFAAAYj8ACAACMR2ABAADGI7AAAADjEVgAAIDxCCwAAMB4BBYAAGA8AgsAADAegQUAABiPwAIAAIz3/xQYLseN1z6gAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "initArgs = {\"funnelWidth\": 10.0, \"rotate\": False}\n", "width = initArgs[\"funnelWidth\"]\n", "nMax = 10\n", "\n", "for systemType, color, marker in zip(\n", " [\n", " FunctionSystemType.FLOW_CYLINDER,\n", " FunctionSystemType.HYPERBOLIC_CYLINDER,\n", " ],\n", " [\"red\", \"green\"],\n", " [\"x\", \"+\"],\n", "):\n", " zeta = SelbergZeta(\n", " functionSystem=systemType,\n", " systemInitArgs=initArgs,\n", " )\n", "\n", " finder = RootFinder(\n", " f=lambda s: zeta(s, nMax=nMax),\n", " algorithmType=AlgorithmTypes.SIMPLE_ARGUMENT,\n", " estimatorType=EstimatorTypes.SUMMATION_ESTIMATOR,\n", " )\n", "\n", " finder.calculateRoots(\n", " reRan=(-0.4, 0.5), imRan=(-0.1, 2.2), precision=(3, 2)\n", " )\n", " for res, order in zip(finder.roots, finder.orders):\n", " print(f\"resonance={res} --> order={order}\")\n", "\n", " plt.scatter(finder.roots.real, finder.roots.imag, c=color, marker=marker)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we repeat the experiment above but now for classical Pollicott-Ruelle resonances calculated from\n", "weighted dynamical determinants with constant weight. From the classical-quantum\n", "correspondence we know that these should coincide with the quantum resonances after a shift by $-1$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "resonance=(-1+1.256j) --> order=2\n", "resonance=(-1-0j) --> order=2\n", "resonance=(-1+0.628j) --> order=2\n", "resonance=(-1+1.885j) --> order=2\n", "resonance=(-1+1.256j) --> order=2\n", "resonance=(-1-0j) --> order=2\n", "resonance=(-1+0.628j) --> order=2\n", "resonance=(-1+1.885j) --> order=2\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# calculate classical resonances for Schottky and flow adapted cylinders\n", "initArgs = {\"funnelWidth\": 10.0}\n", "width = initArgs[\"funnelWidth\"]\n", "nMax = 10\n", "\n", "for systemType, color, marker in zip(\n", " [\n", " MapSystemType.HYPERBOLIC_CYLINDER,\n", " MapSystemType.FLOW_CYLINDER,\n", " ],\n", " [\"red\", \"green\"],\n", " [\"x\", \"+\"],\n", "):\n", " wzeta = WeightedZeta(\n", " mapSystem=systemType,\n", " systemInitArgs=initArgs,\n", " integralType=OrbitIntegralType.CONSTANT,\n", " integralInitArgs={},\n", " )\n", "\n", " finder = RootFinder(\n", " f=lambda s: wzeta(s, nMax=nMax),\n", " algorithmType=AlgorithmTypes.SIMPLE_ARGUMENT,\n", " estimatorType=EstimatorTypes.SUMMATION_ESTIMATOR,\n", " )\n", "\n", " finder.calculateRoots(\n", " reRan=(-1.4, -0.5), imRan=(-0.1, 2.2), precision=(3, 2)\n", " )\n", " for res, order in zip(finder.roots, finder.orders):\n", " print(f\"resonance={res} --> order={order}\")\n", "\n", " plt.scatter(finder.roots.real, finder.roots.imag, c=color, marker=marker)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Funneled Torus Resonances" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We finish our resonance demonstrations with the first couple of resonances for the funneled torus.\n", "These are already rather complicated and not known exactly but there exist previous numerical\n", "investigations in the literature with which we may verify our calculations.\n", "\n", "Again both quantum and classical resonances are calculated and their correspondence can be used as\n", "a consistency check between dynamical determinants and Selberg's zeta function." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# calculate quantum resonances for non-geometric torus coordinate choice\n", "initArgs = {\"outerLen\": 10.0, \"innerLen\": 10.0, \"angle\": np.pi / 2.0}\n", "nMax = 6\n", "\n", "systemType = FunctionSystemType.FUNNEL_TORUS\n", "color = \"red\"\n", "marker = \"x\"\n", "\n", "zeta = SelbergZeta(\n", " functionSystem=systemType,\n", " systemInitArgs=initArgs,\n", ")\n", "\n", "finder = RootFinder(\n", " f=lambda s: zeta(s, nMax=nMax),\n", " algorithmType=AlgorithmTypes.SIMPLE_ARGUMENT,\n", " estimatorType=EstimatorTypes.SUMMATION_ESTIMATOR,\n", ")\n", "\n", "finder.calculateRoots(reRan=(0.08, 0.12), imRan=(-0.0, 25.0), precision=(3, 2))\n", "\n", "plt.scatter(finder.roots.real, finder.roots.imag, c=color, marker=marker)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# calculate classical resonances for non-geometric torus coordinate choice\n", "initArgs = {\"outerLen\": 10.0, \"innerLen\": 10.0, \"angle\": np.pi / 2.0}\n", "nMax = 6\n", "\n", "systemType = MapSystemType.FUNNEL_TORUS\n", "color = \"red\"\n", "marker = \"x\"\n", "\n", "zeta = WeightedZeta(\n", " mapSystem=systemType,\n", " systemInitArgs=initArgs,\n", " integralType=OrbitIntegralType.CONSTANT,\n", " integralInitArgs={},\n", ")\n", "\n", "finder = RootFinder(\n", " f=lambda s: zeta(s, nMax=nMax),\n", " algorithmType=AlgorithmTypes.SIMPLE_ARGUMENT,\n", " estimatorType=EstimatorTypes.SUMMATION_ESTIMATOR,\n", ")\n", "\n", "finder.calculateRoots(\n", " reRan=(-0.92, -0.88), imRan=(-0.0, 25.0), precision=(3, 2)\n", ")\n", "\n", "plt.scatter(finder.roots.real, finder.roots.imag, c=color, marker=marker)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hyperbolic Cylinder Ruelle Distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The genuinely new technique of **PyZeta** is the investigation of invariant Ruelle distributions\n", "via weighted zeta functions. The upcoming plots show such distributions both for the Schottky and\n", "the flow-adapted hyperbolic cylinder. These variants are calculated and visualized with two\n", "different methods namely restriction to the canonical Poincare section and pushforward to the\n", "canonical fundamental domain." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# calculate Ruelle dist at delta-1 for Schottky and flow-adapted systems\n", "FIRST_RESONANCE: Final[complex] = -1.0 + 0.0j\n", "\n", "_, axs = plt.subplots(2, 2)\n", "\n", "for i, integralType in enumerate(\n", " [OrbitIntegralType.POINCARE, OrbitIntegralType.FUNDAMENTAL_DOMAIN]\n", "):\n", " for j, systemType in enumerate(\n", " [MapSystemType.HYPERBOLIC_CYLINDER, MapSystemType.FLOW_CYLINDER]\n", " ):\n", " ruelle = RuelleDistribution(\n", " systemType,\n", " systemInitArgs={\"funnelWidth\": 5.0},\n", " integralType=integralType,\n", " sigma=5e-2,\n", " numSupportPts=600,\n", " )\n", "\n", " firstDistribution = ruelle(\n", " np.array([FIRST_RESONANCE], dtype=np.complex128), nMax=7\n", " )[0]\n", " axs[j][i].imshow(\n", " np.abs(firstDistribution), cmap=\"Reds\", origin=\"lower\"\n", " )\n", " axs[j][i].set_xticks([])\n", " axs[j][i].set_yticks([])\n", "\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The results are quite homogeneous due to the decently large resolution $\\sigma$ as well as the\n", "associated resonance being the first at $\\lambda_0 = -1$. Nevertheless both plots show clearly\n", "the support within the fundamental intervals of the underlying systems." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Funneled Torus Ruelle Distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we complement the invariant Ruelle distributions of the hyperbolic cylinder with similar examples\n", "but now for the funneled torus." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# calculate Ruelle distribution beyond delta-1 for conventional torus params\n", "HIGHER_RESONANCE: Final[complex] = -0.8847\n", "systemType = MapSystemType.FUNNEL_TORUS\n", "systemInitArgs = {\"outerLen\": 10.0, \"innerLen\": 10.0, \"angle\": np.pi / 2.00}\n", "N_MAX = 7\n", "\n", "poincareArgs = {\n", " \"sigma\": 1e-3,\n", " \"refinementLevel\": 0,\n", " \"minusIndices\": [1, 2, 3],\n", " \"plusIndices\": [0, 1],\n", "}\n", "fundamentalDomainArgs = {\n", " \"sigma\": 6e-2,\n", " \"refinementLevel\": 0,\n", "}\n", "\n", "_, (axs1, axs2) = plt.subplots(2, 4)\n", "\n", "for i, axs in enumerate((axs1, axs2)):\n", " for j, (integralType, args) in enumerate(\n", " zip(\n", " [OrbitIntegralType.POINCARE, OrbitIntegralType.FUNDAMENTAL_DOMAIN],\n", " [poincareArgs, fundamentalDomainArgs],\n", " )\n", " ):\n", " ruelle = RuelleDistribution(\n", " systemType,\n", " systemInitArgs=systemInitArgs,\n", " integralType=integralType,\n", " numSupportPts=300,\n", " **args,\n", " )\n", "\n", " higherDistribution = ruelle(\n", " np.array([HIGHER_RESONANCE], dtype=np.complex128), nMax=N_MAX + i\n", " )[0]\n", "\n", " # create a phase-lightness representation of the distribution\n", " absoluteValue = np.abs(higherDistribution)\n", " argument = np.angle(higherDistribution)\n", " hue = (argument + np.pi) / (2 * np.pi) + 0.5\n", " lightness = 1.0 - 1.0 / (1.0 + absoluteValue**0.2)\n", " saturation = 0.8\n", "\n", " rgb = np.array(np.vectorize(hls_to_rgb)(hue, lightness, saturation))\n", " rgb = rgb.swapaxes(0, 2).swapaxes(0, 1)\n", "\n", " axs[2 * j].imshow(np.abs(1.0 - rgb), cmap=\"Reds\", origin=\"lower\")\n", " axs[2 * j].set_xticks([])\n", " axs[2 * j].set_yticks([])\n", "\n", " axs[2 * j + 1].imshow(\n", " np.abs(higherDistribution), cmap=\"Reds\", origin=\"lower\"\n", " )\n", " axs[2 * j + 1].set_xticks([])\n", " axs[2 * j + 1].set_yticks([])\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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Mfv+S/3EzJQB/9tVLOuPL22voe1IYkI3ytx6QKr5Is0jIcm6w++0iGu7NN9x5G5uWAL8NAG+/fdj8thx3pkR+X1nuPiLcPici8haHxZz6Zs5VXfOyqrm5qWA+3e2/GW/KPZ5xvqgJQD1uphl+YLkVBmSj7K0HQMAJePPB232IzcCX/VxvfM4gpClCyw/Bd98+bHZbDr77nNx9e/cRACzs3IhokfUwKEqybskgy4judLs5lO3d/puxptz9FidFRgCyfiutNaBFh2StNhCqDciAzNJb8gzL0mphZM382BBWq4jdfi49LAQyjAwj8GZl+uCFsCpHZrZ6HkLztm62JQxmq49lGJnZ6vtE5C0hg+4B2dPH/Pz037gaLRj87BEcHmF5kYL0rjFL15PegNZPH/GL//wtZtD+6Qn0h806A1p0SNZljWMGDAjpppjcoAAKAytyKHOsyLE8x/MM6gzcsSyHvPlcUWBlQZbnlGbkTUVptgUbFAFgWJ6lchQlpRlFswVz3oSbrHmycyAnfa60NM3QyhIryvstgshD0wRlOzyBn/8Jn//75zwZTSh/8ws4/TytQriTrQMGWY4dnmK/+AV//u9fpw//4hfY8KSZVqgwIGuwgbGDBNLJVgAtg3YA67SxdgtrlVCWWFne9o/neaoEW630Ne02eVHQxmitAsGWtA4YkBepLJ02bQu0LdCyVJbZnRKUzcdazde0Q8DanfTciMgdTaU4eIT/4tcUizn5dIr9uz/FHn/ZhIEd3J/ADEITBv7ib2i5pw2K/vyvsMNTCB/WVaAwIN9vja0Cy0duKQh0DLrBCJ0W1u2sQgHL6XPuUOSrEGCdDqHToZMFOma0mjvnZVfBFsQBrCyg3cY6XVpFQXexoGOBtkXm2GoT5pYZbUvl7JpRFmV6jtrawljkDWapm6DVw57+CR4ybDGH4ydprv2udhPAbbm//EUaJwDY059Bu58+9wEUBuT7ma1tNO5yrEDe3NV3zehboFMWVP0esd/Dxt00fS4LaX5dkWPdLtbvYv0eod/jwAK9kO6YC0vN628PxHuorGwRul3CQZ+i2+NgMqVvga4FFqRBlZB2LexaoG8ZB5aRd3uE/gHW6dxvAUQeGDPDQwZlOzWPtzppb4JWszfBB94hP3Sp3CGV+/hpKitg3QEUrTTeSi0D8tCsxguQ+sk7ZhyEwDAY/bLk+nBAGA7wm5s03XBSNLsWFthBnzAYEA6HlAd9DkNgYCHdMZO6CsKDjwGNVgvr9bDBkHwwYHhxyTBGRu54NKZ3wsAgBIYhY5jlFIMBNhhgvd49F0DkAbKQlhxu99KAwbu7FoZs97oIliykMrZ7WN5KH8uLVdfIh1AYkI1Zjj1YtgwUpMquZ8YwBIZ5xuuDPvFoiE/SFr1eTlPLQFkQDvrY0SHh6JBhnqcwEALdkAbX3W0ZeOisCQNhOCA7PKT//IyjumbcrKJYNq0wHQschsBRyOi1O2SHh4ThEOt277cAIg/QqnUAUvN4MxNpFzcoumtV7ryVWkAglfkjApDCgGzccr58ahkIHFjgOAROQsbLXpfFyTE+m0OWp9353KEoCIMDspNj2sMBJ1nOccialoGQwkAzQ2EbWKuF9fuEw0PCoxM6g+c8ms25cSdgTDwCqeXkOGQ8ygo6gwHh0SPC4SHWVxgQ+V7LsQOrDYnSmh472yqwtCx3eLPcH0phQDYq3blbM5sgVXaDEDgOGY+zjIuYMzk+4rqOWKvEJ1M8RqwsCcMBxeMTjjsdnmQ5JyHjMAR6FlI3wbrHDGzw2mGtFqHfJxwdkT0+JX/yhKObCYuxU1IzWbUMpDBw1OuRP3lC9viUcHRE6PU3d3AiW8wsVYK+3Oxr10NAY93lVhiQjVuOG8hJo+X7FjiyjNOQcZnlXBdOfHTMtN3CbyYQHWuVZP0+R90OnzXB4ThkDEIaaV80i/MEtmStgbLAel3scEg4OSE8eUIxvuFRVVNOp6sw0LXAQbtNcfqY8OQJ4eQEOxxoAKHIj9iXEPC2dZVbYUA2btlNkJOmBfYscBQCj0POTRaZu2MtuCgKpgcHRKC0wEGW8VmW8ZMs50nIeBQyBpY1swkg28CiQ5u6nFhZYt0uYTgknJ6QXY1gNqPtTvHqgjidAhA6bbKjI/IvfkL29DPC6YnGDIjIxikMyEYtBxEG0hK8LQv0gjP0jMdZZE5BDeRmDGNkkuUpDJAGGT7OMp6GnCfNmIF+CLQtdRHcrjOwzqPdDCuKtF7CcJDCwM0kbSoSMsLBAT5JYcA6HcLxEdlPnpJ9/rQJA4O0MJOIyIYoDMj3WucqhMs+/axZirjt1gwizJi7U7uTYwwsMmlG1xdmDCxwkmU8DhknTRfBclphdmehnq1oHMzz2xkFR4ep8q/qtEJav/9mGDgckj19koLA0WGakpjv6OIpIvIgKAzIJ/FGV4EF+sGZkVGTBhi2LHAYItNlGMDoh9Sd8OhOF0FnueBQs8nPVgQBSGuot5qugsNDWFTp40VBGA7x2Qwgrbo4GBBOHpE9PiEcDtNYg1jf37GLyM5TGJA/bk3NA7fb86ZKvAQ6BIZNQsgw2mZcuzN3J8JqgaKBhbQmQcjoNUsRpy6CLRk42LAs4EWBddqEgz7UMa0UVrbww+s0tRJSYGhaD8LRkHBwkJYiXszvuQQisssUBuSTCby5LHFthpMRmkWE+u4smpaBNPMg0LPUQtC3O8sQ32kV2JpA0GxhbGUJ3Q4WI8EM8hzv9273ZViOLTjoYwf9tC9BWWCulgER2RyFAfkB6xs5sKy0A0ZmTumGW8DMyRxKN+buVE0YyJqxAW1Lj06z0NDdPQnWbaPBwgKWZal1oN0mQNpYpSzw2QyvUmVveZ5aBzqdZoOiFhTFbVgQEdkAhQH5pNLSxAZ2u1RxIFDgVAZ1M98+mKUtj5tQUFraqfDutsVrrbw33cRglroFsgwvy/TrQkgbMi06eDMmwEKWPtZqpVaEssDyu6uMiYisn8KAfDJ2520gTSfE06IZOU6NE+12hkDWbEaUN+MEMtvkIkMbTgPLlZeaSZZOiTVdB9Q1FmP6umV3QlGkGQjLILAt6y6LyFZSGJAfts45ho1w5webGcHTtMOIrX7VMjAEbscIbNOWxd+xXCUsLEtvuFkKBDHebhfdtCCQZViWpS2dQ9jpTVdE5P4pDMgftYEc8MZOhsu7fLO0WY87b4QBWw0UtDcGDG7deIG7v8Votl1tlhENIa0tficMLD9OsPS1tpXxR0S2iMKA/Ij1RwJ76/3V8kHmb/wme6slYGNV4qeqZ1fLMRp4APNU+fNWCqLZjtHu7EKmLCAiG6QwIPfi7botA/x7ary7AWAn6kOz1AqwrOQzu20VuPs13/dWRGRDFAbk3rxdxb3dBvF2C8KnO5IN+07lbt/7rkKAiHwqCgPygwzwTQweeOt3wO1Ygu/73E6yuyX/vo+LiHwaCgPyDjacBu78lr2kyl9E7plWMpH9Ztu1x4GIyCYoDMiPstX/RERkFykMyDtSGhAR2VUKA7K/TBFHRAQUBuR9qOYUEdlJCgPyTuzO/3eCsbEtj0REto3CgOwpBQERkSWFAXk/uzAnfgeKICKyTgoD8s5Uh4qI7CaFAXkvu7HmgEYLiIjcpTAg+0UpQETkOxQG5ANs8wR9tQqIiLxNYUDe29ZOM9zmDCMiskEKA/Lhtq5m3boDFhH5JBQG5INsXevAFh2qiMinpjAgH2zbZhZs0aGKiHxSCgPykbagI37bUouIyCeW3/cBiGyU9iAQEflRahmQj7IaO/Bg69sHe2AiIg+GwoB8tAcbCExtAiIi70JhQNbiwc0ueIDZRETkoVIYkLV5MOP0HsyBiIhsB4UBWSvD7nebY1sdhYiIvCOFAVm7VB/fQ3WsICAi8kEUBmQjPnlL/QMOAg/xmERE7lIYkI1ZdRlsujZ8wEEAuN9uExGRd6AwIBu10WmHRlPRPuAgICKyBRQGZOPeCATrqLVXP8fW9iM37WOPcxvKKCLbS2FAPonbdQg+IhTc+T7butaAN56BD/hOEZHN0d4E8snYnfd89QG//QK/80XOW7Xgg1vW6P0sR1S63/7zvb5/a0suIltAYUDuxW2db9/94Nvvf/ef22tZqbv/8Ne9/fUiIhukMCD3am+rOlXyIvKAaMyAiIjInlMYEBER2XMKAyIiIntOYUBERGTPKQyIiIjsOYUBERGRPacwICIisucUBkRERPacwoCIiMieUxgQERHZcwoDIiIie05hQEREZM8pDIiIiOw5hQEREZE9pzAgIiKy5xQGRERE9pzCgIiIyJ5TGBAREdlzCgMiIiJ7TmFARERkzykMiIiI7DmFARERkT2nMCAiIrLnFAZERET2nMKAiIjInlMYEBER2XMKAyIiIntOYUBERGTPKQyIiIjsOYUBERGRPacwICIisucUBkRERPacwoCIiMieUxgQERHZcwoDIiIie05hQEREZM8pDIiIiOy5/L4P4Pu4+30fwvqYYfd9DOvizg69Mph9ulfmY8/pnfqbEJEH597DgAOs8ULnQARqYO7OzJ0bd8buXLtzE50pTu2OAYVBy6BnRt8CvWB0LNDCKMzIAGseH3ZAb1WgBlsTD9ZZ+bunR13jiwrmc/xmQry5xsfX+PU1Pp3iiwW4Y1mGtVtYt4f1ulivn962WlhRQJ5BCPARFfrbFazBR/28H/o9FVDhzB1uPHLtzjhGRu5MPbJoDqUwo23GgRn9EOiZ0bXAdKdimIg8NPceBtbJuQ0DVRMErt25jJFXMXLZvH/jzsIdM6eF0QswtMBxcCoCBAgWME93j4GPCAPfd5BbkgXWyoEYoa5hsUhB4OqKeHFJfP0av7ggXl/DbIq7Y3mBdbuE4RA7HBKOKsKyQjTDgt1W3J/wDv9D1cDCYeKRqxi5aM7J1x4Zxci8CSatJgQcWeDYnTpkWHAqZQER2aCdCgNwJwwAM5ow4M55jLxsLsBjd+buGE7H4MCNWXCcprUAowhOZpABAdvLOnytrQI4RMerGp/P8cmEeDUivnpFPDsnnp8TR1f4dAoxYmWJ9fv4ZEqoKiwEvCiwPIc8X0vLwKcUmwA6dWfkzqsYeRFrXsSaq5g+DtA2Y+jOIqR/Z2a0nLW2nomIvG2nwsCqi6Cp7G+icxUjZ3XNs7rmeYyc1ZErj8w9YkDHYBiMmywQyQhAaUbpRm5G3vzMbM3HuR1V2Bq5p5aBRYVPZ8TRmPjyFfHbF9TPnlE/f45fXhBvblI3QVlgBwOy8TU+n4MFKEooCkJRQpFjyzCwpkCwyddlGU7H7ryONc9jzR/qmmd1xesYV2GgY8ZhyJhlGQ7kTbdBoW4CEdmgnQkDb3QRwKqL4HWMvIiRP9Tp4vsiRi5jZEZqGeiac+jGzNP9f066IHfNaLlRYmS27opiC+LAOu9EvWkVqGt80YwVuLwinr+kfvYt1e+/Ij57lroLJtcpNJQtwnCAT6ZkVY0VBdbpYO023m5jrRKyHEIzFmENgWCTr8jCnYk7oxg5j5Fndc1XdcXXdcWrGJncCQPH7lQ4gabbwIyOWgZEZIPuNQz4nf+v6+dF9zReAGfkqU/2Raz5JtZ8Xdc8r2uu53PqagE4RatglGfUWUZh6WI8CIGBR7oeqCwFhPV2FTzwILBO7k1SS+MFfDbHb27wy0vi2Tn1s2+p//AN9R++prq8ZL6Y4zh5yCivrsjmFWBYp4sNBoSDPhz08aoDRYH5Otts2FhOW5DCwJVHzpuWqq/riq+qisvFgmo+ByAvW1wXBQa0SINaj4NjCgMiskH33zKwpmvcsmWgBhbAjTuX0Tmrm7uwqubrqmJ8cUG8usRnMzBYdNvMDgfUvR6FeWqmtTSA68AiXTcihq+1gtiCloF1aroIvEpdBD4aE1++pv72eQoCX33N+PyMi7pi4jWR1FUzXCwYLmowI3S7xMND4mCADYdkvR6UZRo74OvpKkivymZem7nDuBmzkroIKr6uKs5GI+rXF/hkAsCi22F+dIT1D2hhHITAaQwUUWFARDbnXsOAka7jHxsI/M7b5ZTCm5hmDpzHmm/rmm+rBeNXr6meP8cvL/F5CgPWaeOTG14/fcKzgz4DMx6HjCeeMXFngRO5DRt7VIWvjzteL8cLTImjURov8PwF9TfPuH75imfVgotYc+MRxynNuI5OvB5z9O1zwsGQcHpKPHlEuLnB53Osbt92Z6ypq2BTZr4cLxB5Xtc8izUvr6+pvv2W+Or1KgxYp4NPZ7z8SUa33+e4DrzKMroe77kEAt8zHfUBn3P7ZF9fF19O2YY0y+ojyn3/3QRrbRlI6wfMSWsLXHqaQXBW11xdX1OfnRHPzvCry2ZQWgoDLOZUecarsuA8BF7HmqsYmYTIwjOiLefb78cJtlbLkzVGfLHAJ9PUMvD6gvrsnPmr15xXC85izUWsmXjESS0DM4NQG+XViPz8nOzlK/zyCr+ZpOmJdY3F9Y0ZSDbzGqeZLWlK4XmMvJzNmb98RXxxRnx9kWZRANZuQ1Uzb7d5VZachYyLGDlSN8G989jcFsS4GrjqhL2peB6qVCHG22tNCLhbGmC8w1bljs2NQggfdT7efzfBGkW/bRlYXnhfxprzqqJ6+ZL6/Iz48px4NYJFEwbaLagWUOTcHPQ4K0teZjVX3qxHgFPzZuvDR//p70sTw+pJ8zfXF7hMLQP12Uuubq45qyvOY81lrJl6muJZYMwDZEQ6tqB7/or8/BXx4iItUjSbY1WNN7NC1nvQ639xps3gwVex5jzWjK/HxPNz6vOX+MVF6raiCQOxxjptxgcHnJclr2LkNKpl4D65O8QaYgV1lcJAyCHL8ZApENyTVYVYLdJr4w4hg6zAP/JO+SFbnY91BfUifTArPup83JkwcDuT4HbVwasYeR0j19NJaop9fUG8uMTHo7TSnYHNWukEareoL4aMBgdcFAWjGJl4ZOGptcFtv9YaWM99qK/SuseILyp8MkktAxeXzEdXXFQVrz3N8Lhqptg5UJhTx7TmQz8GTm6uab2+IF6O0gDE2Tz9ISxbBh64adNNcBkjF4sF1XKxpctL4tUVPm26rZahoNdncXnF5cGAy7xgvAVl3FWrC281h/kEFrMUBsoulO007XVHK50Hzz0Fgfk0vTYeoWhB2UktN7sa1NxTCJhNUrkhlbnV/eDzcSfCgN951J4GEE7cGTervVWjMXF0RRyP8OtxWvp2sUhPWFURg2GjDn414mY246rT4dpTxbQcMxD3KQnQjOdY089yd6hjahmYzojX18TRiMX1DVfNCnxjT4tBzZpugqI5gk7zGo7qmsHVFT4ep0CxmONVjcW4FQM65s1U1yt3rqsqrb44GhHHzfk4mwHN+Zjl2GhEvLpivFgwardXUw/lHizDwHyKX5zhl+cQMuzkc8wOIWQ7fRf6UK1C2mKK31ziL7+BqsIGx9jRkzT1eAeD2qo1ZDHDRy/x828AsNMvUtdIlua/va+dCANLaU+CtODQpKlcxjESr8epErm+TneVk8ltGIg1ZAG/viaOxlQ3N4wHg9sw4E6Nr+obeU/LaYXNbAKmU/zmhjgec1NVjGLk2iM3MU29mzUtAwvSyP7r5o56XNfEcbOPwWQK80XqevC7UfDh/tGn1qrIOEZms1k6H8fN+XgzSWNYIJ2PeZHO1fGY6XzOOEZuNIDwHjlUc3z8Cv+Xv4ff/08oSvyXv8F+/pt0Jxqynat0HrxlGJhe41/9M/zuH2A2w7/4Gfzqf8OKVlMx7qC6gskY/9d/hH/+BwD8V3+N/eJ/gaL9QS0iO/NMrQYQcrsvwcQj88WCeDNJAWA6xWezNNe9WmBmaQniIk9T3qZTfDJh2jRXz0kbzMTmZ+/NskPr3KAIv92XoKqapYin+GTKjUemTeiaNt07czz9jQM5aZneiTddNosF5WSaXr9FlX7mch2DByyFm+U56cTJ7fnIbIbPZ/h8sfp6K2/PxTiZMDk8ZP7Ay7jTYoTFHH/xFf5f/iOLf/hnQrckB/z4CdY5gLy876PcQ6mp3K9ewu/+gfo//B31eEbxm3M4PMEOHqWK0XZskKc7xCq1Uv33/8z8//yPEIxWXeMnX2D9Q/DyvcPpzoQBuL0/rEh3lnMnLS40n6WWgMUiTW+rFqliMrBgqS97Pk876c3mzD1tHLMaL9DU3Pt0PV5nN8FqzEDdtA4sFsT5nHlT+c+bhaIq0oY83nxPZek1WHhqZl/Uzb4Gi9Qq4MswsAWvTOXpfJy7pzAzn6duk0UFVfOANCJ4sYD5YnVOzprlteXTux2gNocXf2D+97/ld3/3e3rdnJ89fgS//A32+N9txbiVndMMTPbXL/D/8Tu+/g//H6Pxgj+rI61f/SX8/C/Ta7dzHOoKf/0c/6d/4rd/93sA/up0AH/zv2NPf86HXBN3KgxA6tuPzRTDCifWdaqAqioth1vXqf+6TovZeF1jdZ1OqqrCq2pVMdVvrTEgH2G5N8Gd12PRVP5106JTN++n7GXp35YGhVZAvexqqOr0s5aDB7fgxVkObq3wN85H6jqtwVDXAKvz0evma6qq2f5Y7o1HvJrD2be8+u0L/uvlNYNxxuf/8gdal69Sk63CwP2IFVy9YvGv3/Dfno94uag5/O0Lvjh7ji/m2C6GgeXsrMtXTH77Lf/v5TXBjD/97TN6l69uW0zf086FgWWD/uqxnHt6dx7qqgLxNz/WVC6rFXRXP3H/rK9VgDdPzObfHpfdAcvXa/kf3/tYhrI3Xq8tsixbhO+cb2+U5+3zMfq25J3dFmuYzxiN5zyb11QF1KNJmqK8ixXONlj+nSzm1FcTXlc1z+Y14/Ecn02xWG/ddeLdpXJPR1P+MK8JwGI8hfnsg8/HHQwDqYl79VjuamfNR8zufvLOvw2CNas43X4JPOC+/Q1aWzfB3Sdy9W/DwvJ5tubT1vznqy+7++1h+bE3Xs/tsSxngDfLcPc8/M7n3jwf5R6FDMoWvV7BkyJjkAeyfhvyAr0692T5N1KUZP02h1lGVUKvV2BlueODOlO5W/0WT8u0P0vRbaWdXT/wfNy5MGAYAcgsFS5kAcvT4iCWZ1gW8CxbJUbLMmgeluVYnpNj5BhZ87Pers/kfTV/tCE0z3MGeU4O5AYZRkZ6zTJPcSB749G8HqF5LfMs/axwp0J94AKszqtUhnQ+kmVYaM5Jbs9Hy5qvKZbno9wbC1he4I8ec/LLx/zNyyndbk7586cwPG6msG3BSbiLQgYHRxQ/e8qvH/+Bq9GC0z87hZPPsF0Namapzhoe0/3lZ/yv//gSM+j8+WfN+fhhIWinrjFGqh9yjAKjNCPLCyjLlBSLIu10l+epX9poLrhNkixLrFVShkBpRmFG1tyZLX++fABLS4PaMpiVJaEsaFnaIro0KMzIHaKlnJY3z39h6XUszSiyDCtLrChWleiqxeeBy5sylmZYa3k+prJ4Udw2ZzbnI0WRtmkuW7Sa50E+PTPDLUDegs++pPzbX/GrLBA6Bfbnf3FnPrten0/OLN3kHT+BX/45P/0/XlGNppR/9Ut4+lMo2iks7Jym3EdPsF//Bb9+OQYg/MWd8/EDrok7EwZSlZDuMHNL+8C3zSiKHOu0sXYLa7XSRXixSHeW0ISA5nOdNtbp0A6BdlNRLZdvsDVXOA/60mG2xr42u01py8q83cLabToW6JjRMqMFLCxN2XBLYaDVPNpmdMwoiiK9RmWJFXl6DbegZcBIiyi1LW2Rbe1O82ilc6+c337tMpS221i7Q+i0aTfPg9yTEFJwO/0CfvO3lIeHqTn2F3+BHZ6qq+DeNJXi4BH+p78mq2uy6QR++ifptcoLPnbzngepWQrbDk+wX/01q0mtv/rrdD6GDwunOxMGIFXaWdMq0DGjb0Y/ZLzq9aj7fazXwyaTZs57WtbG2iXW62C9HqHfI+926YeMrgVadttdsB33nw/QajxGlu542y2s1yX0e3TznH4d6MVA1wI1EEgrEOZNAOhZoG+BfpYRlq9hp51aeVbNYQ//1SnN6FqgHwKtdovFQVOWbjdNK1yG01YrfbzXw/p92mWLfgh0d+2CtlUM8hI7OIY/+xv88U8gK7CTz6Hd/+CLr3yk5f4Q7R7201/hnT7UC2x4gg1P0toPtqObFWU5tA+wn/8l9Icp9Jx+kc7HD1xoaSfCwN3qILN04e2YcWDGMBj54IBqMMCvrprd4Ty1DmBYu5UqmUEfGwzotloMQqqAOk3zbCDd2MqHMTM8C1DkWLtN6PUIgwFlt8twPmUQAtceiNHJCURSk3rfAgcWGITAQZYTBgPsoI91O6l1IF+2DvDQswAtM7pmHFignxfcDAaEwQAfjYixhjz9KVq7Tej3CYMBYTigXxQMmvNZ7kkTZik72PHTFArM0lrwZWqK3rm7zy1gzd4DFG2sd5hWHLy7N8GOdt+suq7KFjY4wdq99ImyA2UrjXHZ55aB5UjtnOVdmHEQAoch0G23mR8dEsdjwnxONMMW85Sm2i1sOCAMD8kOh/TLkmFzB9exNHYgM7UMfJjlAL+Qxgwsm/kPethwQHlwwHB0xWGsuLEAwZne2Ztg+fodWUan08UOh4TBAdbtpub0N1oG1njMG9Bqws0wBIZ5zqvhkHg4JI7GhOh4ebuFsQ0HhMMh+WDIIM9X4VTux6rSyZtV3YpW+kSzS9wuVjhboxk3QNlOgfrOroUfWiluBbNUxhZNNxXpeciKDz4f7z8MrG0OW9Mt7al/tWepInkUMk7ygvHJSVrTvq5TE/O8CQOdNmE4IDs9oTsccprlPAoZQ0tNs0UzDmGfpxl+sOVruxz9WhRYt0MYDMgeHZOdPmJw+ZrT0YI5kTw6k2Y2QYlxEDJOs/T6FSfHZCePCIeHWK8HrRLy5SDCdR70ZhaK7phxEIzjEDjJMs76fS5OT8kmU2KWNS1WpPPx6Ihwekq/3+ckyzgOgb6apu7VKhDcHU8Twm5XOFvgjdclZssPrm5AdtUb5Q5NNf6R5+O9hoE15oDbAYTmlA5dMw4tcBICp1nGq26Xi8enuDvWaqWlXg2s0yEcDchPTzlutTkNOcch46BpGSgMwp3Z8Gs72H2xnAv8RsvAAeE4VXitV684mdyw8EgJ3DT7IpRmDCzjNMvpDQdkp6eEk2PscJDGeJRlmoa3nF74wLVILQNHIXAaMp6XLW4ePWI2nUFR4JO0Dal1OoTjY8pHJzxqlZyGjKMQ6Kll4N5ZCLg3YaA55xQE7l/aYyZAFlavzT68LqtyL28UPrLc9xoG1hkElvdzGamfvxuMYdMy8CSLXBQFi6Mjri1QdzpppSYzrNsmHA457Pf5LMt4nGUpDFiaUVBorYGPt1xjIE9jBuygTzg+Int8il9e0L+55unLc9pm3DTdBCXGIMs57PUoHp8SnjwmPDomDAdYp4uVxZvzadf2x7/JbgLjMAQeZxmfxch1r8f5Z59Rt1rfCQNHvR6fhYzHWWjCgM6+h2C1iJk8KLb268B2WOf5eP/dBGuyGkBIqkg6Tf/saQhchoybLEWP58dHjPs94mKBGeRlyaDI+DzL+CLLedp0EwxCoG2B3CzdfN5n4badGXZ3AOFBH390TPb0CT65wRdz+pnRvrxkVi1whyJklL0e2ZPPyL78guzzp4TTE8JwiHU7d2YTrG+/8vRTNtNNUBr0QuDYA09CxlWWNsNiMOCy3aZqtjDOWy2GRcGXWcYXWcaTZcuAuglEZIMeQDfB+joLltPZc6DtaeT2cch4kqWtYyHdoV2EjHm7jeGpOyEYT0Pg8yzn8Z1m2eXUwqCphR/ODMxTpZ1lacGdXjMY8PSUbDpJ20nngfD6gOLmJo0ILluE4ZDw5DOyzz8n++wx4fgozSZot7Aiv7Po0Hqk4Q2beZUL0qDWoQVOs8DYMxbN73sVApNWGpTWsTSuIAXTjNMsMLQUTEVENmXnWgZCs1BQy6DXNMveeMY8c4JBuzYOQ7orM9LFdxiMJyHwWVi2CmR3ZhJsootgG2LFGkd0NE1ZqXWgSE3hgwF+cowv5uQxUhc5NhzgNxNwT2MCDpqxAp99lloFDg9TkGi1UqvAsslmrS0Dm1GY0W5mSDzyjEnmzboKcGDGtNknu9Ocs0+zjM+yjEchcBCMfM+aP0Xk09qZMAC30wszgxLohsAQWOA4OaUZfYuMm/3hDWhbuhifZGlg16OQMViNF0g/b933ZFtxWV/n6E5IFXdoZhR0mnED8+NU8WcB67SJo+PUd+6OFSXW7xOOjwknJ2SnJ2m8QDeNF7Dl/gRbUknmpEGEvebOv/KMgNHCOA7ehAFomzGwwOMs8Dik8Ss9C9txzojI1tqpMABvtQ6QWgcqC8QAhUHXAtceqZotjNM0xHQ3dhTSOINuaPY1aLoIlj9XPpBZChbBUiVeloRuB6pBMy+4Wa//+hpmszTjIy+wbjeNETg8xA6HqVWg3UrzibcoCAAEM0qgQ+DAoApp9kuBMfTIzB1r9mnoW+A4pMdBs+BQtUVlFZHt805hwJu7lqurq7UfgC//v6a70OWe8RXO3KHyiLtTxEjHndqdwp2qaRkojGbt+0Ae0spOczPMApXxxs6Fa2GsfZ+DjWmm+a3rZxEd6hpfLPDFHI8RzzJiu4X3e3ie4fNFahnI87Q0b7eDFXl6DaoKm0zSPuWz/HbnwjUx2EjAcHcqYOHODCdGJ3On5ZF+jGTuLJonujRoW6AVjMwC0YxZCMybv73l3+K2WF07RqN7PhKR/bT82/uxa8c7hYFR88O+/PLLjzwsEfkYo9GI4XB434fxzlbXjl/+5T0fich++7Frh/k73GrEGPnmm284ODjYi8UcRB4ad2c0GvH5558TtmhlNV07RO7Xu1473ikMiIiIyO7anlsMERER2QiFARERkT2nMCAiIrLnFAZERET2nMKAiIjInlMYEBER2XMKAyIiInvu/wfm2HHvFQK+OwAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# calculate Ruelle distribution beyond delta-1 for conventional torus params\n", "HIGHER_RESONANCE: Final[complex] = -0.9998 + 9.12j\n", "systemType = MapSystemType.FUNNEL_TORUS\n", "systemInitArgs = {\"outerLen\": 10.0, \"innerLen\": 10.0, \"angle\": np.pi / 2.00}\n", "integralType = OrbitIntegralType.POINCARE\n", "N_MAX = 6\n", "\n", "poincareArgs = {\n", " \"sigma\": 2e-3,\n", " \"refinementLevel\": 0,\n", " \"minusIndices\": [1, 2, 3],\n", " \"plusIndices\": [0, 1],\n", "}\n", "\n", "_, (axs1, axs2) = plt.subplots(1, 2)\n", "\n", "ruelle = RuelleDistribution(\n", " systemType,\n", " systemInitArgs=systemInitArgs,\n", " integralType=integralType,\n", " numSupportPts=300,\n", " **poincareArgs,\n", ")\n", "\n", "higherDistribution = ruelle(\n", " np.array([HIGHER_RESONANCE], dtype=np.complex128), nMax=N_MAX\n", ")[0]\n", "\n", "# create a phase-lightness representation of the distribution\n", "absoluteValue = np.abs(higherDistribution)\n", "argument = np.angle(higherDistribution)\n", "hue = (argument + np.pi) / (2 * np.pi) + 0.5\n", "lightness = 1.0 - 1.0 / (1.0 + absoluteValue**0.2)\n", "saturation = 0.8\n", "\n", "rgb = np.array(np.vectorize(hls_to_rgb)(hue, lightness, saturation))\n", "rgb = rgb.swapaxes(0, 2).swapaxes(0, 1)\n", "\n", "axs1.imshow(np.abs(1.0 - rgb), cmap=\"Reds\", origin=\"lower\")\n", "axs1.set_xticks([])\n", "axs1.set_yticks([])\n", "\n", "axs2.imshow(np.abs(higherDistribution), cmap=\"Reds\", origin=\"lower\")\n", "axs2.set_xticks([])\n", "axs2.set_yticks([])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We calculated and plotted the same pair of Poincare/fundamental domain approximations for\n", "two subsequent cutoff values $n_\\mathrm{max}$ in the cycle expansion. This helps us verify\n", "that the distributions have indeed converged which beyond the first resonance is often\n", "difficult to make work without symmetry reduction. This is exactly the case for the fundamental\n", "domain variant in our second to last example which has just barely converged.\n", "\n", "In practice it is much cleaner to verify convergence programmatically with one of the error\n", "estimators of **PyZeta**." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.2" }, "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2 }