Index of Examples
Sequence of Successive Preimages
Map
Latex
The Successive Preimages
The Map
Latex code for the map
$ A = \begin{pmatrix} -1 & 1 \\ -1 & 2 \end{pmatrix}, u(x,y) = \Bigl(0.5961575370224703 + 3.977174744332434E-4 \sin(y) + 0.001514099595788044 \cos(y) + 0.0022488064007621174 \sin(2y) + 0.002285551112210198 \cos(2y) + 0.003191433134381192 \sin(3y) + 0.002349332760497439 \cos(3y) + 0.0013840818124867993 \sin(x) + 0.003274760143529914 \sin(x)\sin(y) + 0.0021552445540688444 \sin(x)\cos(y) + 0.0014538245329267453 \sin(x)\sin(2y) + 0.0034799051557367388 \sin(x)\cos(2y) + 0.0017641982140678878 \sin(x)\sin(3y) + 0.00362052603070799 \sin(x)\cos(3y) + 0.004340263820076433 \cos(x) + 0.002547640201678745 \cos(x)\sin(y) + 0.00609577192832049 \cos(x)\cos(y) + 0.004013041119417865 \cos(x)\sin(2y) + 0.0013932416908119473 \cos(x)\cos(2y) + 0.005495746451303638 \cos(x)\sin(3y) + 0.004096022133337028 \cos(x)\cos(3y) + 0.0050038982177165615 \sin(2x) + 0.0012710586804173083 \sin(2x)\sin(y) + 0.0038333563658445005 \sin(2x)\cos(y) + 0.0013195754598367547 \sin(2x)\sin(2y) + 0.0020395865948284837 \sin(2x)\cos(2y) + 0.0011970545813658926 \sin(2x)\sin(3y) + 0.001226627040501076 \sin(2x)\cos(3y) + 0.0053777510693746155 \cos(2x) + 0.0044382753499596726 \cos(2x)\sin(y) + 0.0016898890888611038 \cos(2x)\cos(y) + 0.0027991273021890123 \cos(2x)\sin(2y) + 0.003442564440247645 \cos(2x)\cos(2y) + 0.0059538394153645655 \cos(2x)\sin(3y) + 0.00338423867710693 \cos(2x)\cos(3y) + 0.0021695644231886817 \sin(3x) + 0.006036780582928687 \sin(3x)\sin(y) + 0.0037907145960979645 \sin(3x)\cos(y) + 0.004715826000531686 \sin(3x)\sin(2y) + 0.0037507664541161557 \sin(3x)\cos(2y) + 0.005220664172115711 \sin(3x)\sin(3y) + 2.7716980780832453E-4 \sin(3x)\cos(3y) + 0.0024079633518870034 \cos(3x) + 0.003037917378941884 \cos(3x)\sin(y) + 0.0029391417159945685 \cos(3x)\cos(y) + 0.0025270349535705854 \cos(3x)\sin(2y) + 0.004349851679199423 \cos(3x)\cos(2y) + 0.002205879052284404 \cos(3x)\sin(3y) + 0.0035583901862000266 \cos(3x)\cos(3y) , 0.9357441271834775 + 0.005192911149433618 \sin(y) + 0.0031458832379820407 \cos(y) + 0.00399246948014969 \sin(2y) + 0.004577182741762641 \cos(2y) + 0.006058064761216989 \sin(3y) + 0.004073138337949023 \cos(3y) + 0.0018242495426806162 \sin(x) + 0.002360004655019796 \sin(x)\sin(y) + 0.001853540376673251 \sin(x)\cos(y) + 4.303411874972434E-4 \sin(x)\sin(2y) + 0.002202755537948271 \sin(x)\cos(2y) + 0.0023953162964004122 \sin(x)\sin(3y) + 0.003902630246043657 \sin(x)\cos(3y) + 0.002244009079940868 \cos(x) + 0.004063750515475607 \cos(x)\sin(y) + 0.002056031787558465 \cos(x)\cos(y) + 0.0057515507827214755 \cos(x)\sin(2y) + 0.0032248790494022127 \cos(x)\cos(2y) + 0.0047165987739448585 \cos(x)\sin(3y) + 8.395732497186967E-4 \cos(x)\cos(3y) + 0.0012828307344797444 \sin(2x) + 6.638643114245105E-4 \sin(2x)\sin(y) + 8.375548842453674E-5 \sin(2x)\cos(y) + 0.0048801659111747855 \sin(2x)\sin(2y) + 0.00501736873330328 \sin(2x)\cos(2y) + 0.003460160427285186 \sin(2x)\sin(3y) + 0.001968693779000153 \sin(2x)\cos(3y) + 0.00554273946481328 \cos(2x) + 5.857109928904775E-4 \cos(2x)\sin(y) + 5.630706643478964E-4 \cos(2x)\cos(y) + 0.005220568032870024 \cos(2x)\sin(2y) + 0.0031044969168032856 \cos(2x)\cos(2y) + 0.002022566596505434 \cos(2x)\sin(3y) + 0.004456056998477764 \cos(2x)\cos(3y) + 0.004500655675654879 \sin(3x) + 0.0011220456407560954 \sin(3x)\sin(y) + 0.0038651070844397837 \sin(3x)\cos(y) + 0.004209484965510332 \sin(3x)\sin(2y) + 0.00270255181731298 \sin(3x)\cos(2y) + 0.002694228812720445 \sin(3x)\sin(3y) + 0.0016478470800802263 \sin(3x)\cos(3y) + 8.938343420001022E-4 \cos(3x) + 0.0035882993166833376 \cos(3x)\sin(y) + 0.004626719905051063 \cos(3x)\cos(y) + 0.0026522011753803048 \cos(3x)\sin(2y) + 0.00579820997755139 \cos(3x)\cos(2y) + 0.0011005933694446552 \cos(3x)\sin(3y) + 0.00540239373036243 \cos(3x)\cos(3y)\Bigr)$
