Topological pressure, periodic orbits and invariant measures in differentiable dynamics
Time and place
1 PM on Monday, March 22nd, 2010; NAC 1511
Prof. Christian Wolf (Wichita State University)
Abstract
In this talk we discuss several ergodic-theoretic results for hyperbolic, parabolic, and non-uniformly hyperbolic dynamical systems. These results are based in part on the analysis of the topological pressure, that is, a certain functional on the space of observables, which allows us to make the connection between topological and measure-theoretic dynamics. In particular, we consider non-uniformly hyperbolic systems and show that the topological pressure is entirely determined by the values of the potential on the periodic orbits. We also discuss existence and uniqueness of generalized physical and SRB measures for several classes of systems. Our results are inspired by classical work of R. Bowen, D. Ruelle, A. Manning, H. McCluskey, and others and represent work from collaborations with L. Barreira, K. Gelfert and M. Urbanski
