Special Session 50: Dynamical systems: Oseledets decomposition, ordered spaces, Lyapunov exponents, and applications

Lyapunov--Oseledets spectrum for transfer operator cocycles under perturbations
Cecilia Gonzalez-Tokman
University of Queensland
Australia
Co-Author(s):    Anthony Quas
Abstract:
Random dynamical systems provide useful and flexible models to investigate systems whose evolution depends on external factors, such as noise and seasonal forcing. In recent years, the study of transfer operators has been combined with multiplicative ergodic theory to shed light on ergodic-theoretic properties of such systems. The so-called Lyapunov-- Oseledets spectrum associated to the transfer operator cocycle contains fundamental information about invariant measures, exponential decay rates and coherent structures which characterize dominant global transport features of the system. While the scope of this framework is broad, it is often challenging to identify and approximate this spectrum. In this talk, we present examples of random maps where the Lyapunov-- Oseledets spectrum can be understood and analyzed under perturbations.