## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** Growth rate of periodic orbits for a class of non-uniformly hyperbolic geodesic flows

**Speaker:** Bryce Weaver

**Speaker Info:**

**Brief Description:**

**Special Note**:

**Abstract:**

Using some verifiable properties and local analysis, we are able to construct a Margulis measure on a class of $3$-dimensional non-uniformly hyperbolic geodesic flows, constructed by V. Donnay. The class of metrics can be applied to any surface, in particular $S^2$. This measure is used to obtain precise asymptotics of the growth rate of periodic orbits of the form,
\[ \lim_{t \rightarrow \infty} \frac{ht P(t)}{e^{h t}} = 1,\]
for $\ds h$ equal to the topological entropy and $P(t)$ is the number of periodic orbits of period at most $t$.

**Date:** Thursday, October 27, 2011

**Time:** 4:00pm

**Where:** Lunt 105

**Contact Person:** Prof. Bryna Kra

**Contact email:** kra@math.northwestern.edu

**Contact Phone:** 847-491-5567

Copyright © 1997-2024
Department of Mathematics, Northwestern University.