# Mean Ergodic Shadowing

## TL;DR

This paper introduces mean ergodic shadowing, a new variant of shadowing in dynamical systems, explores its properties and relationships with other variants, and provides conditions for its occurrence.

## Contribution

The paper defines mean ergodic shadowing, analyzes its relationship with existing shadowing variants, and characterizes systems with this property.

## Key findings

- Minimal systems with shadowing lack mean ergodic shadowing.
- A necessary and sufficient condition for orbital limit functions to have mean ergodic shadowing.
- Relationship established between mean ergodic shadowing and other shadowing variants.

## Abstract

We introduce and study a new variant of shadowing namely mean ergodic shadowing. We establish relationship of this variant with several other variants of shadowing. We show that a minimal system with shadowing cannot have mean ergodic shadowing. We give a necessary and sufficient condition for an orbital limit function to have mean ergodic shadowing property.