Corinna Ulcigrai
Title: Non-ergodicity for the Ehrenfest model and other periodic billiards

Abstract: We consider a class of infinite billiards which are Z or ZxZ periodic, which includes the billiard in a strip with periodically spaced barriers and the Ehrenfest wind-tree model, which is a planar billiard with rectangular obstacles placed on the integer grid. The study of these infinite billiards is equivalent to the study of linear flows on abelian covers of compact translation surfaces. We show that, both for almost every parameters and for certain values of the parameters, the flow in almost every direction is not ergodic. Proofs use the reduction of the flow to a skew-product over an interval exchange transformation, the existence of certain coboundaries and properties of the Kontsevich-Zorich cocycle. This is joint work with K. Fraczek.