Dynamical Systems Seminar

Dynamical systems with hyperbolic ("chaotic") behavior can be studied from the statistical point of view by considering an invariant probability measure. The space of such measures is very large and so one arrives at the problem of selecting a measure that is most dynamically relevant. For example, one can prove that there is a unique measure of maximal entropy for transitive subshifts of finite type, which code uniformly hyperbolic systems. I will describe two approaches to this result: one via transfer operators and the other via the specification property. If time permits I will explain how these approaches generalize to other equilibrium states and to more general classes of shift spaces.