{ "cells": [ { "cell_type": "markdown", "id": "031c1ba2", "metadata": { "papermill": { "duration": 0.002139, "end_time": "2026-06-30T01:16:25.220411+00:00", "exception": false, "start_time": "2026-06-30T01:16:25.218272+00:00", "status": "completed" }, "tags": [] }, "source": [ "# Phase-Space Volumes and Chaos\n", "\n", "In addition to integrating orbits, galpy can integrate the *variational\n", "equations*: the linearized equations of motion that govern how an\n", "infinitesimal phase-space displacement $\\delta x$ evolves along an orbit. This\n", "is done with the `Orbit.integrate_dxdv` method, which works for\n", "two-dimensional (planar) and, since version 1.12, fully three-dimensional\n", "orbits, and is implemented in C for most potentials for speed.\n", "\n", "Integrating deviation vectors gives access to the *state-transition matrix*\n", "$M(t) = \\partial x(t)/\\partial x(0)$, whose columns are the evolved\n", "phase-space basis deviations. This allows you to\n", "\n", "* verify **Liouville's theorem** ($\\det M = 1$: phase-space volume is conserved),\n", "* quantify the **sensitivity** of an orbit to its initial conditions, and\n", "* compute **Lyapunov exponents** to detect chaos, using the\n", " `Orbit.lyapunov` method built on top of `integrate_dxdv`.\n", "\n", "This tutorial briefly demonstrates each of these." ] }, { "cell_type": "code", "execution_count": 1, "id": "baa23517", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:16:25.225510Z", "iopub.status.busy": "2026-06-30T01:16:25.225294Z", "iopub.status.idle": "2026-06-30T01:16:27.533081Z", "shell.execute_reply": "2026-06-30T01:16:27.531973Z" }, "papermill": { "duration": 2.311396, "end_time": "2026-06-30T01:16:27.533830+00:00", "exception": false, "start_time": "2026-06-30T01:16:25.222434+00:00", "status": "completed" }, "tags": [] }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy\n", "\n", "from galpy.orbit import Orbit\n", "from galpy.potential import HenonHeilesPotential, MWPotential2014, toPlanarPotential" ] }, { "cell_type": "markdown", "id": "df48b96f", "metadata": { "papermill": { "duration": 0.001363, "end_time": "2026-06-30T01:16:27.537307+00:00", "exception": false, "start_time": "2026-06-30T01:16:27.535944+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Integrating phase-space deviations in 2D\n", "\n", "For a planar orbit, the phase-space deviation is the four-vector\n", "$\\delta x = (\\delta x, \\delta y, \\delta v_x, \\delta v_y)$ in *rectangular*\n", "coordinates (use `rectIn=True`/`rectOut=True` to work entirely in this basis;\n", "otherwise galpy converts from/to cylindrical deviations). `integrate_dxdv`\n", "propagates the deviation with the linearized dynamics along the orbit; the\n", "deviation as a function of time is accessed with `getOrbit_dxdv`.\n", "\n", "Integrating the four basis deviations builds up the state-transition matrix\n", "$M(t)$, and Liouville's theorem says that $\\det M(t) = 1$ at all times:" ] }, { "cell_type": "code", "execution_count": 2, "id": "fa35ad5a", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:16:27.541435Z", "iopub.status.busy": "2026-06-30T01:16:27.541035Z", "iopub.status.idle": "2026-06-30T01:16:27.975090Z", "shell.execute_reply": "2026-06-30T01:16:27.973745Z" }, "papermill": { "duration": 0.437045, "end_time": "2026-06-30T01:16:27.975814+00:00", "exception": false, "start_time": "2026-06-30T01:16:27.538769+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max |det M - 1| = 7.5e-07\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mw2d = toPlanarPotential(MWPotential2014)\n", "ts = numpy.linspace(0.0, 100.0, 1001)\n", "M = numpy.empty((len(ts), 4, 4))\n", "for ii in range(4):\n", " dxdv = numpy.zeros(4)\n", " dxdv[ii] = 1.0\n", " o = Orbit([1.0, 0.1, 1.1, 0.0])\n", " o.integrate_dxdv(dxdv, ts, mw2d, method=\"dop853_c\", rectIn=True, rectOut=True)\n", " M[:, :, ii] = o.getOrbit_dxdv()\n", "detM = numpy.linalg.det(M)\n", "plt.semilogy(ts, numpy.fabs(detM - 1.0))\n", "plt.xlabel(r\"$t$\")\n", "plt.ylabel(r\"$|\\det M(t) - 1|$\")\n", "print(f\"max |det M - 1| = {numpy.amax(numpy.fabs(detM - 1.0)):.2g}\")" ] }, { "cell_type": "markdown", "id": "90ab1e18", "metadata": { "papermill": { "duration": 0.001696, "end_time": "2026-06-30T01:16:27.979560+00:00", "exception": false, "start_time": "2026-06-30T01:16:27.977864+00:00", "status": "completed" }, "tags": [] }, "source": [ "Phase-space volume is conserved to high precision (set by the integration\n", "tolerances) over the whole integration.\n", "\n", "## ... and in 3D\n", "\n", "For three-dimensional orbits, everything works the same with the six-vector\n", "$\\delta x = (\\delta x, \\delta y, \\delta z, \\delta v_x, \\delta v_y, \\delta\n", "v_z)$ and the $6\\times6$ state-transition matrix; the full 3D Hessian of the\n", "potential is implemented in C for most potentials:" ] }, { "cell_type": "code", "execution_count": 3, "id": "717b4c96", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:16:27.984206Z", "iopub.status.busy": "2026-06-30T01:16:27.983988Z", "iopub.status.idle": "2026-06-30T01:16:28.708997Z", "shell.execute_reply": "2026-06-30T01:16:28.707688Z" }, "papermill": { "duration": 0.728385, "end_time": "2026-06-30T01:16:28.709700+00:00", "exception": false, "start_time": "2026-06-30T01:16:27.981315+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max |det M - 1| = 1.1e-07\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ts = numpy.linspace(0.0, 100.0, 1001)\n", "M = numpy.empty((len(ts), 6, 6))\n", "for ii in range(6):\n", " dxdv = numpy.zeros(6)\n", " dxdv[ii] = 1.0\n", " o = Orbit([1.0, 0.1, 1.1, 0.0, 0.1, 0.0])\n", " o.integrate_dxdv(\n", " dxdv,\n", " ts,\n", " MWPotential2014,\n", " method=\"dop853_c\",\n", " rectIn=True,\n", " rectOut=True,\n", " rtol=1e-12,\n", " atol=1e-12,\n", " )\n", " M[:, :, ii] = o.getOrbit_dxdv()\n", "detM = numpy.linalg.det(M)\n", "plt.semilogy(ts, numpy.fabs(detM - 1.0))\n", "plt.xlabel(r\"$t$\")\n", "plt.ylabel(r\"$|\\det M(t) - 1|$\")\n", "print(f\"max |det M - 1| = {numpy.amax(numpy.fabs(detM - 1.0)):.2g}\")" ] }, { "cell_type": "markdown", "id": "6b3af793", "metadata": { "papermill": { "duration": 0.00185, "end_time": "2026-06-30T01:16:28.713761+00:00", "exception": false, "start_time": "2026-06-30T01:16:28.711911+00:00", "status": "completed" }, "tags": [] }, "source": [ "## Lyapunov exponents and chaos\n", "\n", "The growth rate of phase-space deviations is the classic diagnostic of chaos:\n", "for a regular orbit, deviations grow as a power of time, while for a chaotic\n", "orbit they grow exponentially, $|\\delta x(t)| \\sim e^{\\lambda t}$, with\n", "$\\lambda$ the largest *Lyapunov exponent*. `Orbit.lyapunov` estimates\n", "$\\lambda$ using the classic Benettin et al. (1980) method: it propagates a\n", "deviation vector with `integrate_dxdv`, renormalizes it regularly to avoid\n", "overflow, and accumulates the growth factors into the running estimate\n", "$\\lambda(t)$, which is returned at all output times so that you can check its\n", "convergence. For a regular orbit, $\\lambda(t) \\approx \\ln(t)/t \\rightarrow\n", "0$, while for a chaotic orbit $\\lambda(t)$ converges to a positive value.\n", "\n", "The Hénon–Heiles potential is the classic example of a system with a mix of\n", "regular and chaotic orbits. Here we compute the running Lyapunov estimate for\n", "a well-known chaotic and a well-known regular orbit at energy $E = 1/8$\n", "(orbits F and E of [Skokos et al. 2002](https://arxiv.org/abs/nlin/0210053)):" ] }, { "cell_type": "code", "execution_count": 4, "id": "9a1e1ea2", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:16:28.718795Z", "iopub.status.busy": "2026-06-30T01:16:28.718562Z", "iopub.status.idle": "2026-06-30T01:16:30.335535Z", "shell.execute_reply": "2026-06-30T01:16:30.334492Z" }, "papermill": { "duration": 1.620646, "end_time": "2026-06-30T01:16:30.336383+00:00", "exception": false, "start_time": "2026-06-30T01:16:28.715737+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "chaotic: lambda = 0.031\n", "regular: lambda = 0.00027\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hp = HenonHeilesPotential()\n", "ts = numpy.linspace(0.0, 30000.0, 3001)\n", "o_chaotic = Orbit([0.016, 0.0, 0.49974, -numpy.pi / 2.0])\n", "lam_chaotic = o_chaotic.lyapunov(ts, pot=hp, method=\"dop853_c\")\n", "o_regular = Orbit([0.55, 0.0, -0.2417, numpy.pi / 2.0])\n", "lam_regular = o_regular.lyapunov(ts, pot=hp, method=\"dop853_c\")\n", "plt.loglog(ts[1:], lam_chaotic[1:], label=\"chaotic orbit\")\n", "plt.loglog(ts[1:], lam_regular[1:], label=\"regular orbit\")\n", "plt.loglog(ts[1:], numpy.log(ts[1:]) / ts[1:], \"k--\", lw=0.8, label=r\"$\\ln(t)/t$\")\n", "plt.xlabel(r\"$t$\")\n", "plt.ylabel(r\"$\\lambda(t)$\")\n", "plt.legend()\n", "print(f\"chaotic: lambda = {lam_chaotic[-1]:.3f}\")\n", "print(f\"regular: lambda = {lam_regular[-1]:.2g}\")" ] }, { "cell_type": "markdown", "id": "a9767967", "metadata": { "papermill": { "duration": 0.002254, "end_time": "2026-06-30T01:16:30.341802+00:00", "exception": false, "start_time": "2026-06-30T01:16:30.339548+00:00", "status": "completed" }, "tags": [] }, "source": [ "The chaotic orbit's estimate converges to $\\lambda \\approx 0.05$ (consistent\n", "with the literature value for this orbit, e.g., Benettin et al. 1976), while\n", "the regular orbit's estimate decays as $\\ln(t)/t$, the signature of\n", "regularity.\n", "\n", "`lyapunov` works for three-dimensional orbits in the same way and supports\n", "physical outputs: when the orbit and potential carry physical scales, the\n", "returned exponent is in $\\mathrm{Gyr}^{-1}$ (it is a frequency). For example,\n", "for a mildly perturbed disk orbit in `MWPotential2014` (a regular orbit, so\n", "the estimate decays):" ] }, { "cell_type": "code", "execution_count": 5, "id": "3556fd2b", "metadata": { "execution": { "iopub.execute_input": "2026-06-30T01:16:30.347792Z", "iopub.status.busy": "2026-06-30T01:16:30.347586Z", "iopub.status.idle": "2026-06-30T01:16:31.064395Z", "shell.execute_reply": "2026-06-30T01:16:31.063345Z" }, "papermill": { "duration": 0.720897, "end_time": "2026-06-30T01:16:31.065066+00:00", "exception": false, "start_time": "2026-06-30T01:16:30.344169+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lambda(t_mid) = 0.38, lambda(t_end) = 0.21\n", "(decreasing -> consistent with a regular orbit; convergence to zero\n", " requires much longer integration times)\n" ] } ], "source": [ "o = Orbit([1.0, 0.1, 1.1, 0.0, 0.1, 0.0], ro=8.0, vo=220.0)\n", "ts = numpy.linspace(0.0, 1000.0, 101)\n", "lam = o.lyapunov(ts, pot=MWPotential2014, method=\"dop853_c\", renorm_every=5)\n", "print(f\"lambda(t_mid) = {lam[len(ts) // 2]:.2f}, lambda(t_end) = {lam[-1]:.2f}\")\n", "print(\"(decreasing -> consistent with a regular orbit; convergence to zero\")\n", "print(\" requires much longer integration times)\")" ] }, { "cell_type": "markdown", "id": "ee8564a4", "metadata": { "papermill": { "duration": 0.002212, "end_time": "2026-06-30T01:16:31.069823+00:00", "exception": false, "start_time": "2026-06-30T01:16:31.067611+00:00", "status": "completed" }, "tags": [] }, "source": [ "For more details, see the API documentation of\n", "[Orbit.integrate_dxdv](../../reference/orbitintdxdv.rst),\n", "[Orbit.getOrbit_dxdv](../../reference/orbitgetorbitdxdv.rst), and\n", "[Orbit.lyapunov](../../reference/orbitlyapunov.rst)." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.13.14" }, "papermill": { "default_parameters": {}, "duration": 7.425985, "end_time": "2026-06-30T01:16:31.788614+00:00", "environment_variables": {}, "exception": null, "input_path": "doc/source/tutorials/orbits/phase_space_volumes_and_chaos.ipynb", "output_path": "doc/source/tutorials/orbits/phase_space_volumes_and_chaos.ipynb", "parameters": {}, "start_time": "2026-06-30T01:16:24.362629+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }