Analogies between the geodesic flow on a negatively curved manifold and countable Markov shifts

ABSTRACT: By the work of Bowen and Ratner it is known that the geodesic flow on a compact negatively curved manifold can be modeled as a suspension flow over a subshift of finite type. Unfortunately, a symbolic representation is not available if the manifold is non-compact. In this talk I will briefly explain some recent developments on the study of the thermodynamic formalism of the geodesic flow on non-compact negatively curved manifolds. Surprisingly some of the methods used to understand the geodesic flow have consequences to the theory of countable Markov shifts. I will explain such consequences, as well as some open problems.

Date: Jul 09, 2018 at 16:30 h
Venue: Av. Vicuña Mackenna 4860, Macul, La Florida, Región Metropolitana, Sala 2.
Speaker: Anibal Velozo
Coordinator: Italo Cipriano, Cristobal Rivas
Abstract:
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Posted on Jul 5, 2018 in Dynamical Systems, Seminars