Characterization of SRB Measures for Random Dynamical Systems in a Banach space

TL;DR

This paper extends the characterization of SRB measures to $C^2$ random dynamical systems in Banach spaces, showing they satisfy Pesin's entropy formula linking entropy and Lyapunov exponents.

Contribution

It provides a random dynamical systems analogue of Blumenthal and Young's result, establishing conditions under which SRB measures are characterized by entropy and Lyapunov exponents.

Findings

SRB measures satisfy Pesin's entropy formula in the random setting

Conditions under which invariant measures are characterized by entropy and Lyapunov exponents

Extension of deterministic results to infinite-dimensional Banach spaces

Abstract

This paper considers $C^2$ random dynamical systems in a Banach space, and proves that under some mild conditions, SRB measures are characterized by invariant measures satisfying Pesin's entropy formula, in which entropy is equal to the sum of positive Lyapunov exponents of the system. This can be regarded as a random version of the main result in Blumenthal and Young's paper \cite{Young17}.