If GaTech world domination is to be maintained, we need to start taking Poincaré sections of unstable manifolds. Make sure you understand chapters on Discrete time dynamics, Local stability and Cycle stability. — Predrag Cvitanovic 2009-02-11 12:55
It was right in spirit. It was wrong in detail: Jonathan simply used a finite length, straight line segment of the linear eigenvector instead of the curved unstable manifold for initial points, and the axes scales are - as is the custom among the nonlinear graduate students - profoundly mysterious. A return map maps a curvilinear segment labeled by arclength into , i.e., the graph should be a square, with the same units on both axes. “Poincaré return time” is something else.
He never listened to me again, so there it stands. John G's periodic orbit P47.18 in the W03 cell presumably sits very nicely on it.
With Y. Lan I had a bit more luck. He resisted for 6 years or so, but than his wife told him that thesis should be finished this semester and he relented. His Kuramoto-Sivashinsky (“fluid dynamics” in one dimension) plots all like the usual nonlinear garbage:
So I know you can do it, if you get your mind to it.