Title: Periodic approximation of Lyapunov exponents for cocycles over hyperbolic systems
Speaker: Victoria Sadovskaya (Pennsylvania State University)
Abstract: We consider a hyperbolic dynamical systemand a Holder continuous cocycle over with values in , or more generally in the group of invertible bounded linear operators on a Banach space. We discuss approximation of the Lyapunov exponents of in terms of its periodic data, i.e. its return values along the periodic orbits of . For a -valued cocycle , its Lyapunov exponents with respect to any ergodic -invariant measure can be approximated by its Lyapunov exponents at periodic orbits of . In the infinite-dimensional case, the upper and lower Lyapunov exponents of can be approximated in terms of the norms of the return values of at periodic points of . Similar results are obtained in the non-uniformly hyperbolic setting, i.e. for hyperbolic invariant measures. This is joint work with B. Kalinin.