# Preservation of shadowing in discrete dynamical systems

## TL;DR

This paper investigates how various shadowing properties in discrete dynamical systems are preserved under different mathematical constructions like inverse limits, products, and factor maps.

## Contribution

It systematically analyzes the preservation of multiple shadowing notions in discrete dynamical systems under various transformations and constructions.

## Key findings

- Many shadowing properties are preserved under inverse limits and products.
- Certain shadowing properties are not preserved under specific factor maps.
- The study provides a comprehensive framework for understanding shadowing preservation in complex systems.

## Abstract

We look at the preservation of various notions of shadowing in discrete dynamical systems under inverse limits, products, factor maps and the induced maps for symmetric products and hyperspaces. The shadowing properties we consider are the following: shadowing, h-shadowing, eventual shadowing, orbital shadowing, strong orbital shadowing, the first and second weak shadowing properties, limit shadowing, s-limit shadowing, orbital limit shadowing and inverse shadowing.