# Topologically Stable Equicontinuous Non-Autonomous Systems

## TL;DR

This paper establishes conditions under which certain non-autonomous dynamical systems are topologically stable, focusing on properties like equicontinuity, expansiveness, and shadowing in metric spaces.

## Contribution

It provides new sufficient conditions linking equicontinuity, expansiveness, and shadowing to topological stability in non-autonomous systems.

## Key findings

- Mean equicontinuous, mean expansive systems with strong average shadowing are stable.
- Equicontinuous, recurrently expansive systems with almost shadowing are stable.
- Equicontinuous, expansive systems with shadowing are stable.

## Abstract

We find sufficient conditions for commutative non-autonomous systems on certain metric spaces to be topologically stable. In particular, we prove that (i) Every mean equicontinuous, mean expansive system with strong average shadowing property is topologically stable. (ii) Every equicontinuous, recurrently expansive system with almost shadowing property is topologically stable. (iii) Every equicontinuous, expansive system with shadowing property is topologically stable.