Index of Examples
Sequence of Successive Preimages
Map
Latex
The Successive Preimages
The Map
Latex code for the map
$ A = \begin{pmatrix} 1 & 0 \\ 2 & 2 \end{pmatrix}, u(x,y) = \Bigl(0.33865521016464084 + 0.015909801346667037 \sin(y) + 0.00873585877924528 \cos(y) + 0.008500507986790733 \sin(2y) + 0.01064892773694093 \cos(2y) + 0.001977885147779821 \sin(x) + 0.019714595172498094 \sin(x)\sin(y) + 0.011820193675576985 \sin(x)\cos(y) + 0.003863870581410609 \sin(x)\sin(2y) + 0.010350053893102468 \sin(x)\cos(2y) + 0.015744256667358004 \cos(x) + 0.017954965818582108 \cos(x)\sin(y) + 0.005641623984220383 \cos(x)\cos(y) + 0.007556797308163502 \cos(x)\sin(2y) + 0.009288554513332787 \cos(x)\cos(2y) + 0.004453125718676007 \sin(2x) + 0.008899450898740667 \sin(2x)\sin(y) + 0.006991469596001955 \sin(2x)\cos(y) + 0.004108332583259999 \sin(2x)\sin(2y) + 0.005552248877011378 \sin(2x)\cos(2y) + 0.011260686199654524 \cos(2x) + 0.01304898657976882 \cos(2x)\sin(y) + 0.0024543025424333745 \cos(2x)\cos(y) + 0.005935648275949097 \cos(2x)\sin(2y) + 0.008286943212188182 \cos(2x)\cos(2y) , 0.7577380093331052 + 0.002195125227782377 \sin(y) + 0.004589798431647558 \cos(y) + 0.009967145902380988 \sin(2y) + 2.7106582355288287E-4 \cos(2y) + 0.014075899814922892 \sin(x) + 0.013188635292756245 \sin(x)\sin(y) + 0.005168203613369915 \sin(x)\cos(y) + 9.197529857528848E-4 \sin(x)\sin(2y) + 7.887224442431817E-4 \sin(x)\cos(2y) + 0.017436586820343523 \cos(x) + 0.0012669763538199685 \cos(x)\sin(y) + 0.01793373700972418 \cos(x)\cos(y) + 0.011779178220880544 \cos(x)\sin(2y) + 0.008514528850967915 \cos(x)\cos(2y) + 0.0025490225195837087 \sin(2x) + 0.012704736837617097 \sin(2x)\sin(y) + 0.005783393437066181 \sin(2x)\cos(y) + 0.0016668633105710986 \sin(2x)\sin(2y) + 0.005511788492245572 \sin(2x)\cos(2y) + 0.0038968581599673024 \cos(2x) + 0.004620371865850384 \cos(2x)\sin(y) + 0.002413792957281332 \cos(2x)\cos(y) + 0.004879662702200094 \cos(2x)\sin(2y) + 0.00685505679397942 \cos(2x)\cos(2y)\Bigr)$
