Lipschitz shadowing implies structural stability

TL;DR

This paper establishes that for diffeomorphisms, having the Lipschitz shadowing property is equivalent to being structurally stable, and further shows that expansive diffeomorphisms with this property are Anosov.

Contribution

It proves the equivalence between Lipschitz shadowing and structural stability, and characterizes expansive diffeomorphisms with this property as Anosov.

Findings

Lipschitz shadowing is equivalent to structural stability.

Expansive diffeomorphisms with Lipschitz shadowing are Anosov.

Provides a new characterization of structural stability.

Abstract

We show that the Lipschitz shadowing property of a diffeomorphism is equivalent to structural stability. As a corollary, we show that an expansive diffeomorphism having the Lipschitz shadowing property is Anosov.