Existence of SRB measures in chaotic random motions: a graph transform approach

Abstract

SRB measures present a useful class of invariant measures that help understand the chaotic nature of random dynamical systems. Inspired by a paper from Alex Blumenthal and Lai-Sang Young from 2018 titled ”Equivalence of physical and SRB measures in random dynamical systems” this BSc project discusses the existence of SRB measures in chaotic random motions. We look at an innovative geometric construction of SRB measures via a graph transform approach that uses adapted one- sided charts. By pushing forward the stationary measures and approximating the unstable manifolds with pushed forward leaves we show that the sample measures are SRB.