Non uniform expansion and additive noise imply random horseshoe

TL;DR

This paper introduces the concept of a random horseshoe in non-uniformly expanding random dynamical systems with additive noise and proves their density, advancing understanding of complex stochastic dynamics.

Contribution

It defines the notion of a random horseshoe and establishes their density in certain non-uniformly expanding systems with noise, a novel theoretical development.

Findings

Random horseshoes are dense in the considered systems.

The work extends classical dynamical systems theory to stochastic settings.

Provides a new framework for analyzing randomness in complex systems.

Abstract

We propose a notion of random horseshoe and prove density of random horseshoes for non uniformly expanding random dynamical systems with additive noise