Multiplicative Ergodic Theorems and Oceans

Anthony Quas (University of Victoria)

Abstract

I will describe a long-term project concerning mixing rates and oceans. Well-developed Ideas from (time-homogeneous) dynamical systems have been successfully used in conjunction with satellite data to locate slowly mixing regions of the ocean. The project concerns attempts to generalize this to time-varying dynamical systems, where the underlying spectral theory is much less developed. Starting from an analogy with Markov chains, I will introduce Multiplicative Ergodic Theorems on Banach spaces, and I will discuss questions of stability of the Lyapunov exponents (roughly log-eigenvalues) and Oseledets spaces (roughly eigenspaces). This is joint work with Froyland, Gonzalez-Tokman and others