# Meeting Details

Title: Growth rate of periodic orbits for a class of non-uniformly hyperbolic geodesic flows Center for Dynamics and Geometry Seminars Bryce Weaver, visiting Penn State 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 $t$.