Texas A&M University, Department of
Mathematics, 216 Milner Hall, 12th of September 2007, 3:00-3:50
Groups and Dynamics Seminar
Dynamics on an infinite translation surface
W. Patrick Hooper of Northwestern University
A translation surface is a surface built by gluing together polygons in
the plane by translations. Veech made strong statements about the
dynamics of the geodesic flow on translation surfaces built by gluing
together regular n-gons. We will obtain an infinite area translation
surface with infinite genus by applying a limiting process to surfaces
built from regular n-gons and letting n go to infinity. We will
investigate properties of various dynamical systems on this surface. In
particular, we will study the action of the surface's affine
automorphism group, which corresponds to a lattice in SL(2,R).