# On inverse shadowing

## TL;DR

This paper explores the inverse shadowing property in dynamical systems, revealing its strength, implications for system sensitivity, and equivalence to a finite version on compact spaces.

## Contribution

It provides a new reformulation of inverse shadowing, demonstrating its strength and equivalence to a finite version on compact spaces.

## Key findings

- Inverse shadowing systems are not sensitive.
- Reformulation shows inverse shadowing is stronger than initially thought.
- On compact spaces, inverse shadowing is equivalent to a finite version.

## Abstract

We give a reformulation of the inverse shadowing property with respect to the class of all pseudo-orbits. This reformulation bears witness to the fact that the property is far stronger than might initially seem. We give some implications of this reformulation, in particular showing that systems with inverse shadowing are not sensitive. Finally we show that, on compact spaces, inverse shadowing is equivalent to a finite version of it.