Suspension flows over countable Markov shifts.

ABSTRACT: Markov shifts have been systematically used to model discrete time dynamical systems with certain hyperbolicity. In the same spirit suspension flows over Markov shifts model some continuous time systems (e.g. uniformly hyperbolic flows on compact manifolds), where the flow has a transverse section with specified return time. In this talk I will discuss the entropy theory of the suspension flow over a countable Markov shift (a Markov shift with countable alphabet). I will focus on the entropy at infinity of the flow (a natural quantity in the non-compact case) and compactness of the space of invariant measures. I will finish the talk with a few open problems.

Posted on May 28, 2020 in Dynamical Systems, Seminars