Geometry, Topology and Dynamics Seminar
Barak Weiss
Ben Gurion University, Beer Sheva
Parking Garages with optimal dynamics
Abstract: In a celebrated work, Veech showed that so-called "lattice polygons" with an exceptionally large group of affine symmetries exhibit a striking dynamical dichotomy, called the Veech dichotomy.
It is not known whether other (non-lattice) polygons might have the same properties. We construct generalized polygons (`parking garages') in which the billiard flow satisfies the Veech dichotomy, although the associated
translation surface obtained from the Zemlyakov-Katok unfolding is not a lattice surface. We also explain the difficulties in constructing a genuine polygon with these properties.
This is joint work with Meital Cohen. This is a survey lecture, all relevant terms will be defined.
Monday September 19, 2011 at 3:00 PM in SEO 636