# C0-Stability for actions implies shadowing property

## TL;DR

This paper constructs a specific class of stable actions on manifolds and proves that C0-stability guarantees the shadowing property in dimensions two or higher.

## Contribution

It establishes a link between C0-stability and the shadowing property for actions on manifolds of dimension at least two, providing new insights into stability and shadowing.

## Key findings

- C0-stable actions can be constructed explicitly.
- C0-stability implies shadowing property in higher-dimensional manifolds.

## Abstract

We will construct an action $\Phi$, C0 and C1-stable and we will prove that every C0-stable action acting in a manifold of dimensions greater or equal to two, have the shadowing property.