On genericity of shadowing in one dimension

TL;DR

This paper demonstrates that shadowing, a property related to the stability of dynamical systems, is generically present in continuous maps and surjections on a broad class of one-dimensional continua.

Contribution

It establishes the genericity of shadowing in continuous maps and surjections on certain one-dimensional continua, expanding understanding of dynamical stability.

Findings

Shadowing is a generic property in the specified setting.

Applicable to a large class of locally connected one-dimensional continua.

Enhances understanding of stability in one-dimensional dynamical systems.

Abstract

We show that shadowing is a generic property among continuous maps and surjections on a large class of locally connected one-dimensional continua.