## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**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.

**Date:** Tuesday, May 07, 2019

**Time:** 4:00pm

**Where:** Lunt 104

**Contact Person:** Laura DeMarco

**Contact email:** demarco@northwestern.edu

**Contact Phone:**

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