Random minimality and continuity of invariant graphs in random dynamical systems

TL;DR

This paper investigates the existence of continuous invariant graphs in random dynamical systems influenced by both random and deterministic noise, using Lyapunov exponents and new theoretical tools.

Contribution

It introduces criteria based on Lyapunov exponents for the existence of continuous invariant graphs and develops random versions of key ergodic theorems and concepts in topological dynamics.

Findings

Criteria for existence of continuous invariant graphs established

Random semiuniform ergodic theorem developed

Foundational concepts of random topological dynamics discussed

Abstract

We study dynamical systems forced by a combination of random and deterministic noise and provide criteria, in terms of Lyapunov exponents, for the existence of random attractors with continuous structure in the fibres. For this purpose, we provide suitable random versions of the semiuniform ergodic theorem and also introduce and discuss some basic concepts of random topological dynamics.