Random Periodic Solutions of Random Dynamical Systems

TL;DR

This paper defines and proves the existence of random periodic solutions in random dynamical systems, using invariant sets, Lyapunov exponents, and cocycle pullback methods.

Contribution

It introduces a formal definition of random periodic solutions and demonstrates their existence for $C^1$ perfect cocycles on a cylinder.

Findings

Existence of random periodic solutions established.

Use of invariant sets and Lyapunov exponents in proofs.

Application to $C^1$ perfect cocycles on cylinders.

Abstract

In this paper, we give the definition of the random periodic solutions of random dynamical systems. We prove the existence of such periodic solutions for a $C^1$ perfect cocycle on a cylinder using a random invariant set, the Lyapunov exponents and the pullback of the cocycle.