Average shadowing revisited

TL;DR

This paper introduces a new local approach to analyze the shadowing property in diverse dynamical systems, including discontinuous and non-invertible cases, under various perturbations, emphasizing the gluing property for broader applicability.

Contribution

It presents a unifying, local framework based on the gluing property to study shadowing in a wide class of dynamical systems under different perturbations.

Findings

The approach applies to discontinuous systems.

It accommodates non-invertible systems.

It considers large perturbations.

Abstract

We propose a novel unifying approach to study the shadowing property for a broad class of dynamical systems (in particular, discontinuous and non-invertible) under a variety of perturbations. In distinction to known constructions, our approach is local: it is based on the gluing property which takes into account the shadowing under a single (not necessarily small) perturbation.