Dynamics in eigendirections of pseudo-Anosov maps on certain doubly periodic flat surfaces

Geometry Topology Seminar
Monday, September 12, 2011 - 2:05pm for 1 hour (actually 50 minutes)
Skiles 005
Martin Schmoll – Clemson U
Dan Margalit
We consider particle dynamics in the (unfolded) Ehrenfest Windtree Model and theflow along straight lines on a certain folded complex plane. Fixing some parameters,it turns out that both doubly periodic models cover one and the same L-shaped surface.We look at the case for which that L-shaped surface has a (certain kind of) structure preservingpseudo-Anosov. The dynamics in the eigendirection(s) of the pseudo-Anosovon both periodic covers is very different:The orbit diverges on the Ehrenfest model, but is dense on the folded complex plane.We show relations between the two models and present constructions of folded complex planes.If there is time we sketch some of the arguments needed to show escaping & density of orbits.There will be some figures showing the trajectories in different settings.