EVENT DETAILS AND ABSTRACT

Title: A criterion for unique ergodicity of a translation flow
Speaker: Professor Yitwah Cheung
Speaker Info: San Francisco State University
Brief Description:
Special Note:
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.