Shadowing, chain transitive sets with nonempty interior and attractor boundaries

TL;DR

This paper investigates shadowing phenomena in $C^1$-dynamics, improves results on hyperbolic sets, and explores the stability of attractor boundaries, providing new insights into dynamical systems behavior.

Contribution

It advances understanding of shadowing and attractor boundaries in $C^1$-dynamics, offering improved results and additional findings compared to prior research.

Findings

Enhanced results on hyperbolic sets in $C^1$-dynamics

New insights into the stability of attractor boundaries

Derived several supplementary results in the field

Abstract

We examine certain phenomena in $C^1$-dynamics from a viewpoint of shadowing and improve a known result on hyperbolic sets. We also review a result on the stability of attractor boundaries from the same viewpoint and derive several additional results.