Geometry, Topology and Dynamics Seminar
Yitwah Cheung
San Francisco State University
A criterion for unique ergodicity of a translation flow.
Abstract: Consider a polygon in the plane symmetric with respect
to the origin. Glueing each pair of opposite edges by
a translation map we obtain a closed surface carrying
a flat metric with cone points. The vector field given
by $\Dot{x}=0, \Dot{y}=1$ generates an area-preserving
(measureably invertible) flow in the vertical direction.
The flow is said to be uniquely ergodic if normalised
Lebesgue measure is the unique Borel probability measure
invariant under it. Using the Delaunay decomposition
for flat surfaces and Veech's zippered rectangles we
shall arrive at a general condition in terms of the
original polygon that implies the flow in the vertical
direction is unique ergodicity.
This is joint work with Alex Eskin.
Monday April 3, 2006 at 3:00 PM in SEO 512