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