EVENT DETAILS AND ABSTRACT

Title: Ergodic theory of interval exchange transformations
Speaker: Howard Masur
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

Interval exchange transformations and the closely related straight line flows on translation surfaces are interesting examples of dynamical systems. It has been known for a long time that there are examples of IET (and equivalently straight line flows) that are minimal but not uniquely ergodic. There are also known bounds for the number of invariant ergodic probability measures. There are also examples of IET with a generic invariant measure which is not ergodic. This means it has a generic point. Ergodic measures themselves are certainly generic. Recently V. Cyr and B. Kra gave bounds for the number of the number of generic measures for subshifts with linear growth in the number of words of length n. A Corollary of their work are bounds for the number of generic measures in the case of IET. In this talk I will indicate how their bounds can be improved in some cases of IET and translation surfaces. The goal of the talk will be to review the history of the subject and indicate how the tool of Teichmuller dynamics is helpful.