Lyapunov exponents in random dynamical systems and how to find and use them for bifurcation problems

This talk aims to give an overview on various notions of Lyapunov exponents (LEs) in random dynamical systems, depending on the timescale one wants to study: from finite-time LEs to classical asymptotic LEs and corresponding spectra up to LEs for processes conditioned on staying in bounded domains. We demonstrate how these notions become relevant in the context of stochastic bifurcations, in finite and infinite dimensions.