Topological Stability of Random $cw$-Expansive Systems with Shadowing

M. Oliveira; R. Bilbao; E. Santana

Topological Stability of Random $cw$-Expansive Systems with Shadowing

Dynamical Systems 2026-07-11 v1

Authors: M. Oliveira , R. Bilbao , E. Santana

Abstract

This paper investigates the topological stability of random dynamical systems . Our main goal is to extend the classical result of Walters \cite{Walters77} to the random setting by employing the notions of random continuum-wise expansivity and shadowing property. We prove that any random dynamical system that is random $cw$ -expansive and satisfies the random shadowing property is randomly topologically stable. Furthermore, in the random setting we establish the topological invariance of these properties under conjugacy and analyze the relationship between topological transitivity and the periodic shadowing property.

Keywords

random dynamical systems topological stability continuum-wise expansivity shadowing property topological transitivity

Cite

@article{arxiv.2607.10505,
  title  = {Topological Stability of Random $cw$-Expansive Systems with Shadowing},
  author = {M. Oliveira and R. Bilbao and E. Santana},
  journal= {arXiv preprint arXiv:2607.10505},
  year   = {2026}
}