| 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). |
