{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Orbits of rotations"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By default, we will represent points in the circle by numbers in the interval $[0,1)$. The following function `to_unit_circle` converts from these coordinates to the unit circle.\n",
"\n",
"Here is a Sage version of the function:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"to_unit_circle(x) = (cos(2*pi*x), sin(2*pi*x))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is a way to write the function more in the spirit of Python:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def to_unit_circle(x):\n",
" return (cos(2*pi*x), sin(2*pi*x))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The two ways of writing a function should be roughly equivalent in this notebook, but the Sage version allows you to do somethings you can't do in Python such as take derivatives."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here is an example of the use of the function above:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1, 0)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"to_unit_circle(0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that the output of the last command in a block is automatically printed in Jupyter."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0, 1)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"to_unit_circle(1/4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below we define a rotation of the interval $[0,1)$ by $\\frac{2}{5}$."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"T(x) = x + 2/5 - floor(x + 2/5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we test it:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2/5"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"T(0)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1/5"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"T(4/5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following is a function that computes the forward orbit of $x$ under $T$ up until time $N$. So, this returns the list of values\n",
"$$[x,T(x), \\ldots, T^N(x)].$$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"def forward_orbit(x, T, N):\n",
" orbit = [x] # Start of the orbit.\n",
" y = x\n",
" for i in range(N):\n",
" y = T(y) # Redefine y to be T(y)\n",
" orbit.append(y) # Add y at the end of the orbit.\n",
" return orbit"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we see that $0$ has a periodic orbit of least period $5$:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[0, 2/5, 4/5, 1/5, 3/5, 0]"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"orbit = forward_orbit(0,T,5)\n",
"orbit"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0\n",
"2/5\n",
"4/5\n",
"1/5\n",
"3/5\n",
"0\n"
]
}
],
"source": [
"for x in orbit:\n",
" print(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following converts orbit into circle coordinates:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[(1, 0),\n",
" (-1/4*sqrt(5) - 1/4, 1/4*sqrt(-2*sqrt(5) + 10)),\n",
" (1/4*sqrt(5) - 1/4, -1/4*sqrt(2*sqrt(5) + 10)),\n",
" (1/4*sqrt(5) - 1/4, 1/4*sqrt(2*sqrt(5) + 10)),\n",
" (-1/4*sqrt(5) - 1/4, -1/4*sqrt(-2*sqrt(5) + 10)),\n",
" (1, 0)]"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"circle_orbit = [to_unit_circle(x) for x in orbit]\n",
"circle_orbit"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can plot the `circle_orbit`:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"Graphics object consisting of 1 graphics primitive"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"line2d(circle_orbit, aspect_ratio=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we plot two orbits:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"Graphics object consisting of 2 graphics primitives"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plt1 = line2d(circle_orbit, aspect_ratio=1)\n",
"orbit2 = forward_orbit(1/3, T, 5)\n",
"circle_orbit2 = [to_unit_circle(x) for x in orbit2]\n",
"plt2 = line2d(circle_orbit2, aspect_ratio=1, color=\"red\")\n",
"plt1 + plt2 # Addition combines plots"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A more sophisticated way to deal with rotations."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following function gives returns the rotation by alpha."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"def rotation(alpha):\n",
" def T(x):\n",
" val = x+alpha\n",
" return val - floor(val)\n",
" return T"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"R = rotation(5/8)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below we plot an orbit:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"Graphics object consisting of 1 graphics primitive"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"orbit = forward_orbit(1/3, R, 8)\n",
"circle_orbit = [to_unit_circle(x) for x in orbit]\n",
"line2d(circle_orbit, aspect_ratio=1, color=\"red\", axes=False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## An irrational orbit:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will now consider the rotation by $\\sqrt{2}-1$."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"sqrt(2) - 1"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"alpha = sqrt(2)-1\n",
"alpha"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The following defines $T$."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"T = rotation(alpha)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"sqrt(2) - 1"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"T(0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We compute an orbit of length 100 and then plot it."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"orbit = forward_orbit(0,T,100)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"circle_orbit = [to_unit_circle(x) for x in orbit]"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"Graphics object consisting of 1 graphics primitive"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"line2d(circle_orbit, aspect_ratio=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Remark. The above code ran into problems when I defined $T$ to be\n",
"\n",
"T(x) = x + alpha - floor(x + alpha)
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we compute and plot an orbit of length 1000."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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+QbzPPtZJKAX4NWGC/2vU930BTjVD0KL8oVueLSvLNgeSJYxH873PDN55x/cVkBZx+u47TlkRfe+/L61e7fcaXstg0yYe1UPd3XNPfD9YMxm3dTtQV7Nm+R3f6zLRokU+R0caxLUEKsrKcr8Olo5QFytW+B3f68zg9dd9jo6kS0IRVJTJ+J/qI7l+/3u/43stA463RG18/33yiqBcixbJ/bXBr4YN/S45ei0DpsWoqUxGat48nGuNGjVKXbp0Ua9evcK5YAUUAmrq66/9bu3jbTuKwkIpN9fHyEgqqw/I6m5H4QPfMKEmXn5ZOussP2N7mxmsW+drZCRRWr9TTuuvG7Wzfr2/sb2VwXPP+RoZSZP2D8S0//pRfXff7W9sb2UQ1oEMiDc+CB1+H1Admzb5G9tbGbzyiq+RkRR8AP4Yvx/YmUWLtp2/ETRvZTB3rq+RkQQzZ1oniCYKATvj62VeL2Xw/fc+RkWSdOtmnSC6vvvOOgGibO1aP+N6KYOwzuxEPPHdb9X22MM6AaLM1xK8lzJgCQCVoQiqh98nVGb6dD/jeikD/iADdcdup9iRvfbyM66XMhg1yseoiDu+SagZ3k7Gjkyc6OcbBS9lMGeOj1ERZ99+a50gnihQ7EhpafBjBl4GmYzUqVPQoyLufE1tgTT64ovgxwy8DDZskL76KuhREWdbt1oniDdmB9iejyc2Ay+DkpKgR0Tc1fN+0jaQLj7uJwX+15T7Baho5UrrBMnA7AAVTZsW/JiBlwHnHqOiVq2sE1TO8nAboC6WLAl+zMAPt/nZz6QPPwxyRMRZHL6jtTzcpqZ43BSSNGRI8McEBD4z4EkilItDEQBx9PzzwY8ZeBnk5wc9IgCgogMPDH7MwMugQ4egRwRQjtkWJOnzz4N/ZDvwMhg9OugREUd8aAF+FRcHO17gZXDEEUGPCADYXtAPEwReBu+/H/SIACq67jrrBIiCpUuDHS/QMmBpAPBvxAjrBIiCoN/sD7wMGjUKckTEEd8UAP4FvRNwoGWwcSN7EwFAGII+az7QMqAIACAcmzcHO16gZeDjwAUAwE8FvXNK4MtEAAD/5s0LdrxAy4BDTIBwTJpknQDW9t032PECLYOmTYMcDUBlBg60TgBrn34a7Hj1a/OTMpmMioqKfvLfv/mmznmQAIWF1gmqVlJSopIKTzuU/1kujHpwoILZs6v+u5aTk6OsGrymXKvzDMr3fwcARFNNz+eoVRlUNjOYMWO9jjuOtaK0Kyio3v/Xq1cvffzxx3W6Vm3G2H5msHLlSvXu3Vtz585V69atQ81SlzH4fiztHtbSpedX+oFf05lBrZaJsrKydhggLy9LUk5thkSCVPebkezs7DqfLBbEGOVycnLqNFaYvx4e1oA0R82aNQvsz3+gN5CDfgkCyTZs2LBIjBGUMH89t9xS50sh9oJ90SDQM5Dnzi3SgQcyM0i7uO1NtGzZMrVt21ZLly5VmzZtrONUC2chQxqmgoI/RXNm0LRpwyCHA0LR6N+7KzZil0XEyNChvQP9M1urewaVad6cv0yIH8oAcTRgwIWB7hId6MygQYMgRwMAVCbol3wDLYNddgl+8yTED3tUAf4deGCw4wVaBllZ0X/7FP7tuqt1AiD51q0LdrzAz0AG4BdPEkGS9tkn2PECLYPXXntNLVp8EuSQAIAd2GuvVho/fnxg4wVaBsXFxVq/PuCFLMRS3N41AOLnp1sC1UWgZXDBBRfo4ot3CXJIxFQ9FiC92LLFOgGioHFjSdoQ6JiB/5UN+qYGgG14fBuSn/tGgZdBu3ZBjwgAqMjHE3u1LoOxY8eqadOmP3xNmzZNknTooYFlQ8zx1EuwFi60ToCoOO204Mes9XYUP//5z3XYYYf98OPyfeBLS+seCsBPdexonQBRsWhR8GPWugxycnKUk/PTHUpZJkJFvXpJdTzvxZtRo0Zp1KhR2srhAIiZoUOlKVOCHTPQewZr165VWdmcIIdEzM2YYZ2gcsOGDdPcuXPrfDpZGFhyQ0VffLFMkrRo0SLNmjVLS5YsqfOYgZbBhAkTdOSRvYIcEgnwyCPWCYBkufPOSyVJ119/vbp3764//vGPdR4z0MNtyvXoIc2cGfSoiLMov4RWWFio3NzcGh8gHhZmBdjeypVSq1bBjunl1aAvv/QxKuKM5+OB4ETq0dKq9OzpY1TEGW/O1g6zAmwvL8/PUQFeyuCii3yMirjjg61m7r7bOgGiaM89/YzrpQzYzx6VmTXLOkF83HijdQJEka/PVy9lsP/+PkZFEnTvbp0gHphFoTIDB/oZlzJA6Pigqxq/P6hKrMqgYUMfoyJJ+MDbsbVrrRMg6po39zOut13n99vP18hIiscft04QPS1aWCdAlDVpInXq5Gdsb2Vw1VW+RkZSXH45519UxGwJO1NcLGVn+xnbWxnswoFnqIbddpPKyqxT2KMIUB1Nm/ob21sZDBrka2QkTXZ2uguBIkB19evnb2xvZZCb62tkJFF2tlRQYJ0ifBQBauK66/yN7XWZiNkBaqJ5c2n0aOsU4aEIUBPZ2dIhh/gb31sZSFLjxj5HRxJdeml4H5KjRo1Sly5d1KtXuNuuz5hBEaDmtm71+7SZly2syz35pHTJJb5GR9KFte11mFtYUwKorfPOk5591t/4XmcGffv6HB1Jl5UlzUnQwXkUAepiwAC/49f6DOTq8PVyBNKjfI00yofj7AwlgCD4fpHX68wgK0s6+mifV0BaZGXF792VlSspAgTn0EP9ju+1DCTpggt8XwFpUVLiPlwfftg6SdXKylzOvDzrJEiK00/39+ZxOe9l0Lmz7ysgbYYNcx+2Bx1kneTHVqxwuXz/pUX67Lab/2t4fZpIcscdcv4tfKvLn+K6Pk3EUhB8W7DA/zfW3mcG9etLQ4b4vgrSLitr21cYN5srXg/wrVUr/9fwXgaSvzM7gR2pV+/HH9YbNtR9zIrjUQAIU4MGUk6O/+uEUgbDh4dxFWDHmjT56Yd5xa/yfbRycyv/fwArY8aEcx1mBgAQYfvuG851QimDhg2ZHQBATXXs6HdzuopCKQNJ6tIlrCsBQDK0bRvemfKhlcHAgWFdCQCSwef5BdsLrQzy8qSf/zysqwFA/B1zTHjXCq0MJKlHjzCvBgDx1aRJOI+Ulgu1DM46K8yrAUB83XdfuNfzvh3F9po2lYqLw7wisDOFknIlFUjye7gNUF2rVkktW4Z3vVBnBpI0dGjYVwSAeGnZMtwikAzK4LLLwr4iAMTLiBHhXzP0MujenTeSAaAqP/tZ+NcMvQwk6dxzLa4KANHXrJnUoUP41zUpg5tvtrgqAETf00/bXNekDMp3iQQA/JjFEpFkVAZZWdJJJ1lcGQCi66KLwn+KqJxJGUh2UyEAiKowt5/YnlkZ7LGH/zM9ASAu8vKks8+2u75ZGUjSuHGWVweA6OjdW2rc2O76oW9HUdHmzVKjRlZXB8qxHQXszZ4tHXyw3fVNZwYNG0pPPmmZAADsDRokde1qm8G0DCTp+OOtEwCArUGD3FOWlszLoE0bqX176xQAYKNDB2nIEOsUESgDSfrb36wTAICN/v3d1v7WTG8glysrk7KzrVMgvbiBDDuLF0vt2lmniMjMoF49acoU6xQAEK7rrotGEUgRKQPJPWMLAGli+ZLZ9iJTBk2bSpdfbp0CAMJx5plSnz7WKbaJTBlI0t138xIagHQYOtT+cdKKIlUGubnSgAHWKQDAv6jt3BypMpCkxx+3TgAAfr33nlS/vnWKH4tcGey1l+02rgDgW5TuFZSLXBlInHUAILkmT47mvdFIlkHbtlK/ftYpACB4Rx1lnWDHIlkGkjRmjHUCAAjWxInSLrtYp9ixyJZB+/bSrbdapwCA4Bx7rHWCykW2DCR3ODQAJMHTT7szXKIq0mXQpo00cqR1CgCom/79pXPPtU5RtUiXgSQNHmydAADqZvjw6L1XsL3Il0HLltL111unAIDaGTo0HjsrROI8g50pLZUOO0yaOdM6CZKJ8wzgz5w59ucbV0fkZwaS1KCBdNVV1ikAoGaOPDIeRSDFZGYgSZmMuwHzwgvWSZA8zAwQvJwcafly9884iMXMQHJbvd54o3UKAKieK66ITxFIMSoDSerWTbrzTusUAFC1vn2lO+6wTlEzsVkmKldUJDVjJo9AsUyEYL31lnTiidYpaiZWMwPJTbuefdY6BQDs2G9+E78ikGI4Myh3zDHugAig7pgZIDhr1ki7726douZiNzMo99hjUtOm1ikAYJvRo+NZBFKMy6BzZ24mA4iOo46SLr7YOkXtxXaZSJK2bHEvpAF1wzIR6iY3V5oxQ+rUyTpJ7cV2ZiC5jZ8++8w6BYC0u/feeBeBFPMykKSDDpKuu846BYC0atw43stD5WJfBpJ7uSMOuwICSJbGjd3qRL0EfJIm4JfgzhR94AHrFADS5vbbpY4drVMEIxFlIEkHHCDddJN1CgBpcfHF0q9+ZZ0iOLF+mmhHrrxSevRR6xSIF54mQs2tWCHtvbd1iuAkZmZQ7rbb4vvSB4B4eOaZZBWBlMAy2GMPadIk6xQAkuqcc6QLLrBOEbzElYEk9eol3XefdQoASXPKKdJzz1mn8CNx9wwqat9e+uYb6xSIPu4ZoHpWrZJatrRO4UciZwblpk61TgAgKSZPTm4RSAkvg332kRYssE4BIO5uuCH5L7Ymugwkt7vpDTdYpwAQV61bx+8Iy9pIfBlI0l13SX/4g3UKAHHTq5f05ZduU8ykS/QN5Io2b3bvHxQXWydB9HADGT9Vv740a5Z04IHWScKRipmBJDVsKH3+ubTfftZJAMTBtGnpKQIpRWUgSe3auTcHAaAqI0ZIffpYpwhXqspAknr3lj75xDoFgKi6/Xbp2mutU4QvdWUgST16SNdfb50CQNS0aSMNHy5lZVknCV8qy0Byx9SNGGGdAkBUDBwoff21u7+YRql5mmhHMhnp+OOlKVOsk8AWTxOl3SGHSG+/7Ta6TKvUzgwkNxWcMEH6xS+skwCw9NZb6S4CKeUzg3Jr10otWlingB1mBmn2ySfuPmLapXpmUK78ZbSePa2TAAjT8uUUQTnK4N923VV64w3rFADCkJ0tjR8v5eVZJ4kOyqCCVq3cPiRdulgnAeDTpEnSqadap4gWymA7nTpJ48ZZpwDgy3PPSf37W6eIHm4gV2LTJqlxY+sUCAc3kNNixgzuDVaGmUEldtlFWrzYOgWAoLz6KkVQFcqgCu3aSYsWuT3NAcTXW29JZ5xhnSLaWCaqhpUrpUMPlVassE4CP1gmSrJPP5W6d7dOEX3MDKph773d88jNm1snAVAT77xDEVQXZVADCxdKgwdbpwCwM506STNnSsccY50kPlgmqqHiYunww6XPPrNOguCwTJQ0CxZInTtbp4gXZgY11KSJNHu2OwADQLT06+fOO6cIao4yqIWsLOm//1u66SbrJADKdewoTZwoNWhgnSSeKIM6uO02ty4JwNZDD0nz5rn3g1A7lEEddevGmcqApaeekq66Sqpf3zpJvFEGAejRQ8rPlwYNsk4CpMu770oXXpjOM4uDRhkEZM893evuN9xgnQRIvgED3O4A/fpZJ0kOHi314I9/lG691ToFqo9HS+OkSxe34RwbSQaLMvBk2TKpbVvrFKgeyiAuXnvNnUNQjzWNwPFb6kmbNq4Qmja1TgLE3/77S1OnSqefThH4wm+rR61bS+vWSQ8/bJ0EiK9DDpGmTJH69rVOkmyUgWfZ2dIvf+meeuCtSKBmnn7avcvDWcX+UQYh6ddP+uAD95YkgKp17y69/740dCiPjYaFMghRy5bS/PnS+PHWSYDo6tNH+sc/pKOOsk6SLpRByLKz3dMQ8+a5Z6UBOG3bSq+8In34odSwoXWa9OHRUkMlJdLVV0uPP26dJO14tNRat27Sm29yb8ASMwNDjRpJjz0mvfiidRLAzptvcpM4CiiDCBg8WNq0Sbr7bt5LQHoMHy5995100knWSSCxTBQ5X3whDRniDtBBWFgmClNurvS//8vGjlHDzCBiDjhAmjVLevll6yRA8K65xr2ISRFED2UQUWedJa1fL91xh3USoO4OOkgqKpIefNA6CSpDGURYkybS7372CFSTAAAEgklEQVTnDs/5xS+s0wA1d9BB0ujRbtmT+2HRxj2DGHn6aemii6xTJBH3DILWqJH7s/rAAxxFGReUQcxs2CC99ZZ09tnWSZKEMgjSkUe6x0Wb8VsZKywTxcyuu7r7CWvXukPAgSiZNs19UQTxQxnE1G67ubeXV66UbrnFOg3S7Nxz3V5CmYybFSCeWCZKiG++kc45x/2lRE2xTFQbZ54pDRvmduRlZ9H4owwSZvVq6bTT3HbZqC7KoCaaNZPGjZOOOYYSSBKWiRJmjz2kv//dvdjDa/4IUtu27g35deukY4+lCJKGMkio3Fz3REd+vnskFaitPn2kpUulJUvcWcSUQDKxTJQS69dL06dL/ftbJ4kilol2ZPRo6fjj3YwAyUcZpExZmbvZfPLJbsoPiTL4sffek3r25I3htGGZKGXq1ZM6dJDmzpWWL3ff/QGHHy4tW+a+WTj6aIogjZgZQKWlbpZwxRVpfTQ1vTODSZOk3r3deytIN2YGUIMG0sEHSx995B5NfeklTp1KsvPPd08ElZVJAwdSBHCYGaBSy5ZJzz7rdk5NtmTPDOrVk044wW1f0q6dVL++dSJEEWWAavniC/eo6g03WCfxIZllcOyx0o03SgMGWCdBHFAGqLEFC6QxY1xBvP66dZogJKMMevaUuneXLrhAOuwwt400UF2UAeokP1/6v/+T5s+X7r3XOk1txbcMmjVzxbz//u7IVF4IQ21RBghMaam0Zo10113SE09IGzdKW7dap6qO+JRB//7S7rtLN98stW7t3jQHgkAZwKsPPnBvPn/8sfTCC9ZpKhPdMujY0e0M2q6dKwLOCYAvlAFCU1bmnlCaPFmaONH9OBr3HKJTBr/7nfvO/7jjpK5defIH4aEMYKqkRCoqkl57TXr3XSk7Wxo7NuwU4ZfB7ru7J7Oys90Rps2buy/ACmWASNqwQVq8WJo1Sxoxwr0M9913UufO0uzZQV/NTxmccoq0YoU7GL5pU3eTt2tXqUkTbvQieigDxE5pqSuL+fNdYRQVSQsXrtUdd/xd5557uCZMaKn166UePaRPP5V22UXatKmqEasugyZNpOJi9+9HH+3e1B4yxI3ZsKHUrZv7yspy/2zQgA98xA9lgNgYO3asrrjiih9+PHHiRPXt21eStHjxYnXo0EEzZ85Ut27dfvTzMhn3wV1SIm3ZIt122/168MGRciXQUtIqSWv08ccFat26mUpLt32g16vHBzvSgTJAbBQVFSk/P/+HH7du3VqNGzeWVHUZbK+kpEQlJSU//LiwsFBt27ZVQUGBmvG4DlKKZxUQGzk5OcrJyanzOI0aNVIjXs8FfoQyQKytXbtWS5Ys0YoVKyRJ8+fPlyS1atVKrVq1sowGxApbWCPWJkyYoO7du+vkk0+WJJ1zzjnq3r27HnnkEeNkQLxwzwCpV1hYqNzcXO4ZINWYGQAAKAMAAMtEgDKZjIqKipSTk6MsXihASlEGAACWiQAAlAEAQJQBAECUAQBAlAEAQJQBAECUAQBAlAEAQJQBAECUAQBA0v8DBLdu+G3bgyQAAAAASUVORK5CYII=\n",
"text/plain": [
"Graphics object consisting of 1 graphics primitive"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"orbit = forward_orbit(0,T,1000)\n",
"circle_orbit = [to_unit_circle(x) for x in orbit]\n",
"line2d(circle_orbit, aspect_ratio=1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Of course, the full infinitely long forward orbit of any point is dense, as we will prove in class. Also see Devaney's Theorem 3.13."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 8.6",
"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": "2.7.15"
}
},
"nbformat": 4,
"nbformat_minor": 2
}