Extensions of Expansive Dynamical Systems

TL;DR

This paper studies how expansive and Anosov systems can be extended, providing stability results and methods to embed systems with shadowing properties, advancing understanding of their structural behavior.

Contribution

It introduces new techniques for extending expansive systems, including embedding systems with shadowing, and establishes stability results for extensions of Anosov systems.

Findings

Extensions of expansive systems can be constructed with shadowing properties.

Stable extensions of Anosov systems are characterized.

Any expansive system can be embedded into one with shadowing.

Abstract

We characterize and describe the extensions of expansive and Anosov homeomorphisms on compact spaces. As an application we obtain a stability result for extensions of Anosov systems, and show a construction that embeds any expansive system inside an expansive system having the shadowing property for the pseudo orbits of the original space.