EVENT DETAILS AND ABSTRACT

Title: Symbolic dynamics for three dimensional flows with positive topological entropy
Speaker: Yuri Lima
Speaker Info: University of Mayland
Brief Description:
Special Note:
Abstract:

Since Hadamard, the construction of symbolic models for dynamical systems has been successfully implemented in many scenarios. E.g. geodesic flows on surfaces of negative curvature are coded by suspensions over finite Markov shifts.

In a joint work with Sarig, we deal with flows with positive speed on three dimensional manifolds. These include geodesic flows on surfaces, and Reeb vector fields. Provided the flow has positive topological entropy, we code it by a suspension over a countable Markov shift.

Here is an application: for almost every metric on the two-sphere, there are C,h>0 such that there are at least Ce^{Th}/T closed geodesics of size at most T.