{ "cells": [ { "cell_type": "markdown", "id": "031c1ba2", "metadata": { "papermill": { "duration": 0.004022, "end_time": "2026-06-10T01:05:00.729842+00:00", "exception": false, "start_time": "2026-06-10T01:05:00.725820+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": "2026-06-10T01:05:00.739033Z", "iopub.status.busy": "2026-06-10T01:05:00.738665Z", "iopub.status.idle": "2026-06-10T01:05:07.032127Z", "shell.execute_reply": "2026-06-10T01:05:07.025232Z" }, "papermill": { "duration": 6.299496, "end_time": "2026-06-10T01:05:07.033125+00:00", "exception": false, "start_time": "2026-06-10T01:05:00.733629+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": 0.005163, "end_time": "2026-06-10T01:05:07.041004+00:00", "exception": false, "start_time": "2026-06-10T01:05:07.035841+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": "2026-06-10T01:05:07.055584Z", "iopub.status.busy": "2026-06-10T01:05:07.054993Z", "iopub.status.idle": "2026-06-10T01:05:07.660271Z", "shell.execute_reply": "2026-06-10T01:05:07.659095Z" }, "papermill": { "duration": 0.61257, "end_time": "2026-06-10T01:05:07.661323+00:00", "exception": false, "start_time": "2026-06-10T01:05:07.048753+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": 0.00297, "end_time": "2026-06-10T01:05:07.667754+00:00", "exception": false, "start_time": "2026-06-10T01:05:07.664784+00:00", "status": "completed" }, "tags": [] }, "source": "Phase-space volume is conserved to high precision (set by the integration\ntolerances) over the whole integration.\n\n## ... and in 3D\n\nFor three-dimensional orbits, everything works the same with the six-vector\n$\\delta x = (\\delta x, \\delta y, \\delta z, \\delta v_x, \\delta v_y, \\delta\nv_z)$ and the $6\\times6$ state-transition matrix; the full 3D Hessian of the\npotential is implemented in C for most potentials:" }, { "cell_type": "code", "execution_count": 3, "id": "717b4c96", "metadata": { "execution": { "iopub.execute_input": "2026-06-10T01:05:07.675341Z", "iopub.status.busy": "2026-06-10T01:05:07.675082Z", "iopub.status.idle": "2026-06-10T01:05:08.550515Z", "shell.execute_reply": "2026-06-10T01:05:08.549298Z" }, "papermill": { "duration": 0.881583, "end_time": "2026-06-10T01:05:08.552293+00:00", "exception": false, "start_time": "2026-06-10T01:05:07.670710+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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", 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" ] }, "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": 0.004723, "end_time": "2026-06-10T01:05:08.562051+00:00", "exception": false, "start_time": "2026-06-10T01:05:08.557328+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 H\u00e9non\u2013Heiles 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": "2026-06-10T01:05:08.573354Z", "iopub.status.busy": "2026-06-10T01:05:08.573142Z", "iopub.status.idle": "2026-06-10T01:05:10.753990Z", "shell.execute_reply": "2026-06-10T01:05:10.752757Z" }, "papermill": { "duration": 2.189031, "end_time": "2026-06-10T01:05:10.755988+00:00", "exception": false, "start_time": "2026-06-10T01:05:08.566957+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "chaotic: lambda = 0.055\n", "regular: lambda = 0.00027\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "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": 0.005342, "end_time": "2026-06-10T01:05:10.767394+00:00", "exception": false, "start_time": "2026-06-10T01:05:10.762052+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": "2026-06-10T01:05:10.780394Z", "iopub.status.busy": "2026-06-10T01:05:10.780129Z", "iopub.status.idle": "2026-06-10T01:05:11.355299Z", "shell.execute_reply": "2026-06-10T01:05:11.354124Z" }, "papermill": { "duration": 0.584225, "end_time": "2026-06-10T01:05:11.357266+00:00", "exception": false, "start_time": "2026-06-10T01:05:10.773041+00:00", "status": "completed" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lambda(t_mid) = 1.18, lambda(t_end) = 1.06\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": 0.005511, "end_time": "2026-06-10T01:05:11.368640+00:00", "exception": false, "start_time": "2026-06-10T01:05:11.363129+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": "3.13.12" }, "papermill": { "default_parameters": {}, "duration": 13.788456, "end_time": "2026-06-10T01:05:12.094476+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": "2026-06-10T01:04:58.306020+00:00", "version": "2.7.0" } }, "nbformat": 4, "nbformat_minor": 5 }