Julien Sedro (LPSM, Paris): Quenched linear response for expanding on average cocycles

BudWiSer - The Budapest - Wien Dynamics Seminar 

Abstract: After recalling what is linear response in a deterministic setting, I will explain how one can generalize this notion for non-autonomous systems, notably for random compositions of uniformly expanding maps. Recently, in a joint work with Davor Dragicevic and Paolo Giulietti, we established a linear response result under a weaker expanding on average condition, which allow us to choose randomly among families containing neutral or contracting maps. The proof relies on the study of the Lyapunov spectrum of a transfer operator cocycle, and on ad-hoc perturbation results.