{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Using Sage for computations with interval exchange transformations\n", "====================================\n", "\n", "Vincent Delecroix, CNRS, LaBRI (Bordeaux, France)\n", "\n", "This worksheets is available in notebook and pdf format from http://www.labri.fr/perso/vdelecro/teaching.html\n", "\n", "Short history\n", "--------------\n", "\n", "A lot of computer experiments have been done since the 90's to understand better interval exchange transformations and translation surfaces:\n", "- computation of Rauzy classes (Arnoux, Zorich)\n", "- Lyapunov exponents of the Kontsevich-Zorich cocycle (Kontsevich, Zorich)\n", "- volumes and Siegel Veech constants (Eskin)\n", "- square tiled surfaces (Lelièvre)\n", "\n", "(... and some younger experimentators: V. Delecroix, C. Fougeron, P. Hooper)\n", "\n", "Want to learn Sage? Make some computations related to research projects?\n", "------------------------------------------------------------------------------\n", "\n", "Sage days:\n", "- (past) Oaxaca Mexico may 2016\n", "- dynamical system Marseille summer school july 2017 (P. Arnoux )\n", "- Grenoble summer school june 2018 (E. Lanneau )\n", "- Toronto end of june 2018 (A. Randecker )\n", "- more?\n", "\n", "If interested, get in touch with me (Vincent Delecroix ) and the organizers.\n", "\n", "About this worksheet\n", "----------------------\n", "\n", "The aim of this presentation is to explain how to play with Birkhoff sums over interval exchange transformations using the `surface_dynamics` package. We will mainly illustrate the following theorem of B. Adamczewski\n", "\n", "Let $T: [0,1] \\to [0,1]$ be a self-similar interval exchange transformation with renormalization matrix $M$. Let $f: [0,1] \\to \\mathbb{R}$ be a mean zero function that is constant on each continuity interval of $T$. Then the Birkhoff sum $$S_n(f, x) = f(x) + f(Tx) + \\ldots + f(T^{n-1} x)$$ is either bounded or $$\\max_{k < n} |S_n(f, x)| \\sim C\\ n^\\theta\\ \\log(n)^k$$ where\n", "\n", "- $C$ is some positive constant\n", "- $\\theta = \\log(|\\lambda'|) / \\log(|\\lambda|)$ is the ratio of logarithms of two eigenvalues of $M$ and\n", "- $k \\in \\{0, 1, 2, \\ldots\\}$ is the size of some Jordan block with eigenvalue $\\lambda'$.\n", "\n", "**remark:** On the one hand, Adamczewski theorem can be considered as a baby case of more general results about Birkhoff sums over generic i.e.t. (Zorich, Forni, Bufetov). But it is important to notice that the conclusion of Adamczewski theorem is much more precise than what is known for generic i.e.t.." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from surface_dynamics.all import *" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0 1 2 3\n", "3 2 1 0" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p = iet.Permutation((0,1,2,3), (3,2,1,0))\n", "p" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 338, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# creating a number field\n", "x = polygen(QQ) # variable of polynomial\n", "poly = x^4 - 7*x^3 + 13*x^2 - 7*x + 1 # polynomial\n", "emb = max(poly.roots(AA, False)) # embedding\n", "K = NumberField(poly, 'a', embedding=emb) # number field\n", "a = K.gen() # generator of number field" ] }, { "cell_type": "code", "execution_count": 341, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "4.3902568845155136046636000979379800686395248281747" ] }, "execution_count": 341, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# a is an exact number!\n", "a.n(digits=50)" ] }, { "cell_type": "code", "execution_count": 344, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# choose some lengths\n", "lengths = vector((-a^3 + 7*a^2 - 13*a + 7,\n", " a^3 - 6*a^2 + 8*a - 4,\n", " -2*a^3 + 12*a^2 - 15*a + 4,\n", " 2*a^3 - 13*a^2 + 20*a - 6))" ] }, { "cell_type": "code", "execution_count": 346, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(-a^3 + 7*a^2 - 13*a + 7, a^3 - 6*a^2 + 8*a - 4, -2*a^3 + 12*a^2 - 15*a + 4, 2*a^3 - 13*a^2 + 20*a - 6)\n", "(0.227777104234381, 0.0952939852239145, 0.199668914067685, 0.477259996474020)\n" ] } ], "source": [ "print lengths\n", "print lengths.n()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 262, "metadata": { "collapsed": false }, "outputs": [], "source": [ "T = iet.IntervalExchangeTransformation(p, lengths)" ] }, { "cell_type": "code", "execution_count": 263, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AkWgAAACKRAMAAFAkGgAAgCLRAAAAFIkGAACgSDQAAABFogEAACgSDQAAQJFoAAAAikQD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\n6Bpd95yGvr6+9Pb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"text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "execution_count": 263, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T.plot_two_intervals()" ] }, { "cell_type": "code", "execution_count": 264, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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qKqZNm8a2bdvo2rUrixYt4thjjwVg69atH5ognHDCCbz44ovceuutnHHGGeTn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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 264, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T.plot_function()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 265, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# plotting an orbit\n", "G = T.plot(interval_height=0.4)\n", "x = 1/2 # initial point\n", "for i in range(5):\n", " y = T(x)\n", " G += line2d([(x,0.4),(y,-0.4),(y,0.4)], linestyle='dashed', alpha=0.2)\n", " G += circle((x,0.4), radius=0.01, color='black', fill=True)\n", " G += text(\"$x_{%d}$\"%i, (x,0.34))\n", " x = y" ] }, { "cell_type": "code", "execution_count": 270, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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rstHGr8Xb29pUR1Ae3k8lr+I9RlJuZgYYHtan4gsReRsTIyl35IicNxsasqeA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\ntCjbvMt7w4AAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 31 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G.show(figsize=(6,4), axes=False)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 347, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2, 3, 0, 3, 2, 3, 0, 3, 1, 3]\n" ] } ], "source": [ "x = 1/2\n", "coding = []\n", "for _ in range(10):\n", " coding.append(T.in_which_interval(x))\n", " x = T(x)\n", "print coding" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 272, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def birkhoff_sums(T, x, n):\n", " bsums = [[0],[0],[0],[0]]\n", " for _ in range(n):\n", " i = T.in_which_interval(x)\n", " for j in range(4):\n", " bsums[j].append(bsums[j][-1] + (i==j))\n", " x = T(x)\n", " return bsums" ] }, { "cell_type": "code", "execution_count": 273, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[[0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4],\n", " [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],\n", " [0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3],\n", " [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8]]" ] }, "execution_count": 273, "metadata": {}, "output_type": "execute_result" } ], "source": [ "birkhoff_sums(T, 1/2, 16)" ] }, { "cell_type": "code", "execution_count": 274, "metadata": { "collapsed": false }, "outputs": [], "source": [ "b0, b1, b2, b3 = birkhoff_sums(T, 1/2, 100)\n", "L0 = line2d(list(enumerate(b0)), color='blue')\n", "L1 = line2d(list(enumerate(b1)), color='red')\n", "L2 = line2d(list(enumerate(b2)), color='green')\n", "L3 = line2d(list(enumerate(b3)), color='purple')" ] }, { "cell_type": "code", "execution_count": 275, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KwS9bob7LVqjwbYwwAAAAuBlbocKfMMIAAADgRr9shdqerVDhHxhhAAAAcKP/boU6IGUA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\nVDCIiIiIiEi2VDCIiIiIiEi2/h98JoNRvZQ0CwAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "execution_count": 275, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(L0 + L1 + L2 + L3)" ] }, { "cell_type": "code", "execution_count": 276, "metadata": { "collapsed": false }, "outputs": [], "source": [ "norm_lengths = vector(lengths) / sum(lengths)" ] }, { "cell_type": "code", "execution_count": 277, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n = 100\n", "b0, b1, b2, b3 = birkhoff_sums(T, 1/2, n)\n", "L0 = line2d(list(enumerate(b0)), color='blue') + \\\n", " line2d([(0,0),(n, norm_lengths[0]*n)], color='blue', linestyle='dashed')\n", "L1 = line2d(list(enumerate(b1)), color='red') + \\\n", " line2d([(0,0),(n, norm_lengths[1]*n)], color='red', linestyle='dashed')\n", "L2 = line2d(list(enumerate(b2)), color='green') + \\\n", " line2d([(0,0),(n, norm_lengths[2]*n)], color='green', linestyle='dashed')\n", "L3 = line2d(list(enumerate(b3)), color='purple') + \\\n", " line2d([(0,0),(n, norm_lengths[3]*n)], color='purple', linestyle='dashed')" ] }, { "cell_type": "code", "execution_count": 278, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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MNx4MwOWYYQAAAHbZ+MlGHV99XA8uf9DusiApbz0DXQEoNjiHAQAAFFry0WQt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y/9gt5Wz8DPBlp6KGZVVATbt6sgYd06df/Utav6AN1gANsyzNCYGPjokyKeeyeS5WdCCd0cyumr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\nctTum8GDS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"text/plain": [ "Graphics object consisting of 8 graphics primitives" ] }, "execution_count": 278, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(L0 + L1 + L2 + L3)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 279, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def extrema(bsum):\n", " mins = [(0,0)]\n", " maxs = [(0,0)]\n", " for i,s in enumerate(bsum):\n", " if s < mins[-1][1]:\n", " mins.append((i,s))\n", " if s > maxs[-1][1]:\n", " maxs.append((i,s))\n", " mins.append((len(bsum),mins[-1][1]))\n", " maxs.append((len(bsum),maxs[-1][1]))\n", " return mins,maxs" ] }, { "cell_type": "code", "execution_count": 288, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 42.9 s, sys: 409 ms, total: 43.3 s\n", "Wall time: 42.9 s\n" ] } ], "source": [ "%%time\n", "# this takes about a minute\n", "n = 1000000\n", "R = RealField(128)\n", "Tnum = iet.IntervalExchangeTransformation(p, T.lengths().change_ring(R))\n", "b0, b1, b2, b3 = birkhoff_sums(Tnum, 3/7, n)\n", "l0, l1, l2, l3 = norm_lengths.n()\n", "b0 = [x - i * l0 for i,x in enumerate(b0)]\n", "b1 = [x - i * l1 for i,x in enumerate(b1)]\n", "b2 = [x - i * l2 for i,x in enumerate(b2)]\n", "b3 = [x - i * l3 for i,x in enumerate(b3)]\n", "L0 = line2d(list(enumerate(b0)), color='blue')\n", "L1 = line2d(list(enumerate(b1)), color='red')\n", "L2 = line2d(list(enumerate(b2)), color='green')\n", "L3 = line2d(list(enumerate(b3)), color='purple')" ] }, { "cell_type": "code", "execution_count": 289, "metadata": { "collapsed": false }, "outputs": [], "source": [ "opts = dict(linestyle='dotted', alpha=0.8)\n", "m0, M0 = extrema(b0)\n", "m1, M1 = extrema(b1)\n", "m2, M2 = extrema(b2)\n", "m3, M3 = extrema(b3)\n", "E0 = line2d(m0, color='blue', **opts) + line2d(M0, color='blue', **opts)\n", "E1 = line2d(m1, color='red', **opts) + line2d(M1, color='red', **opts)\n", "E2 = line2d(m2, color='green', **opts) + line2d(M2, color='green', **opts)\n", "E3 = line2d(m3, color='purple', **opts) + line2d(M3, color='purple', **opts)" ] }, { "cell_type": "code", "execution_count": 290, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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370q0VCleVissAMA77xiXiYmR3UYHGm/FiIQEZzsFdpkwQT7WLig0b+6sTqug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\nCIIgCCeEwuDVqt1ly4AWLazrXreOqzRJHniU9O/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KDIV86ZJ6W1dd5b4vL0EmnLo9fvhh+IJCRImEhATUr18fTZo0wdy5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\naWnO84wJ3gYM8H+/R486n3RS9LA2FgD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R2iL/OuWdAaFGwsf5Hxnn+n551hUjWuS5diimwi1qrk+8zik3NjLWyfxHfY/K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\nKGq7/7/7iF4Xje8ufydqTz+ZjrgtcZJrDPh0ADblbBK17Tq/C9HroiX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IgiCMoZCpMxr/t/E/Rnmb0W14r9FXFnRzFhQXQy/tTfo1Mfk+X4R+AY82HhDYCdDgowa8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\nCp7rs8z4mBlSu3BjoGZlz5JVVZ0QQog040r0/j9/f3+Ul+vPlOLm5oY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"text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "(L0 + E0).show(figsize=(8,2))\n", "(L1 + E1).show(figsize=(8,2))\n", "(L2 + E2).show(figsize=(8,2))\n", "(L3 + E3).show(figsize=(8,2))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 330, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9lQ8AAKiyLpWG66+/vrdyAAAANapL3wgNAAC89SgNAABAIaUBAAAopDQAAACF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\n53bp8b3hhba2/OSJJ6odYxu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VO9Iwd+7cTJkypVLDAQAAPcSnJwEAAIWUBgAAoJDSAAAA\nFFIaAACAQkoDAABQSGkAAAAKlcrlcrk3B1i1alVGjBiR1tbWvO1tb+vNoQDe8jZs2JBly5Zl3Lhx\nGThwYLXjUKfMo+3zulCrKjE3e700rFu3Li0tLVm7dm2am5t7cygAAKAXOD0JAAAopDQAAACFlAYA\nAKCQ0gAAABRSGgAAgEIVKw0zZ87M9OnTM2/evEoNCQAA9AAfuQoAABRyehIAAFBIaQAAAAr1+ulJ\n5XI569evzx577JFSqdSbQwEAAL2g10sDAABQ35yeBAAAFFIaAACAQkoDAABQSGkAAAAKKQ0AAEAh\npQEAACikNAAAAIX+fzlvuhPxoJQrAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 83 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# the iet we started with is a self similar iet\n", "TT = iet.IntervalExchangeTransformation(p, vector(lengths) / lengths[0])\n", "T.plot_towers(iterations=0).show(aspect_ratio=0.28)\n", "TT.plot_towers(iterations=8).show(aspect_ratio=0.1)" ] }, { "cell_type": "code", "execution_count": 334, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[1 1 1 1]\n", "[1 2 0 0]\n", "[0 0 2 1]\n", "[2 3 2 2]" ] }, "execution_count": 334, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# the iet was actually constructed from a loop in\n", "# the Rauzy diagram (Rauzy, Veech)\n", "path = 'ttbtbbtb'\n", "R = p.rauzy_diagram()\n", "g = R.path(p, *path)\n", "eigs = sorted(g.matrix().eigenvalues())\n", "eigs\n", "g.matrix()" ] }, { "cell_type": "code", "execution_count": 337, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.411385002063387" ] }, "execution_count": 337, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# By Adamczewski this should be the exponent of the polynomial \n", "# growth rate of trajectories\n", "log(eigs[-2].n()) / log(eigs[-1].n())" ] }, { "cell_type": "code", "execution_count": 336, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.35740080964063825, 0.3574832506498919, 0.3575656056590716, 0.3576478748471031, 0.3270146466709104]\n", "[0.327059355553862, 0.3272467348559632, 0.32758194506161326, 0.32776797413339925, 0.3276987634854622]\n", "[0.34382373312399106, 0.3439476174660387, 0.3440724487609351, 0.3441970650826055, 0.34412446026940924]\n", "[0.3758928077121051, 0.3760304170592185, 0.37630555875050753, 0.3764424472099946, 0.3441991608613851]\n", "[0.27534251950091365, 0.275617968732891, 0.2761086502624149, 0.27638141305292535, 0.2527083563384629]\n", "[0.2516033718369013, 0.25170517989437097, 0.251806844855031, 0.2519083671200714, 0.25185530280137497]\n" ] } ], "source": [ "print [log(abs(float(y)))/log(float(x)) for x,y in m1[-5:]]\n", "print [log(abs(float(y)))/log(float(x)) for x,y in M1[-5:]]\n", "print [log(abs(float(y)))/log(float(x)) for x,y in m2[-5:]]\n", "print [log(abs(float(y)))/log(float(x)) for x,y in M2[-5:]]\n", "print [log(abs(float(y)))/log(float(x)) for x,y in m3[-5:]]\n", "print [log(abs(float(y)))/log(float(x)) for x,y in M3[-5:]]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.0.beta9", "language": "", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }