Comparison of entropy for infinite covering manifolds, and group extensions of subshifts of finite type

Abstract: A classical example of an Anosov flow is the geodesic flow associated to a compact hyperbolic manifold M, for which the periodic orbits of the flow correspond to closed geodesics in M. In general, Anosov flows are not so well behaved: there may be infinitely many periodic orbits in a free homotopy class, in contract to geodesic flows. In this talk we discuss the problem of counting periodic orbits in infinite covering manifolds, where we relate the exponential growth rate of periodic orbits in the cover to properties of the covering group. One of the tools is a new result for non-symmetric group extensions of subshifts of finite type which includes a result on non-symmetric random walks. I will spend some time motivating the problems and give the perspective of the thermodynamical formalism. (Featuring joint work with Richard Sharp.)

dynamical systems

Audience: researchers in the topic

Bremen Online Dynamics Seminar

Series comments: Talks are approx. 55 min plus discussion. Talks are not recorded.

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