Product Anosov diffeomorphisms and the two-sided limit shadowing property

TL;DR

This paper characterizes product Anosov diffeomorphisms through the two-sided limit shadowing property, linking universal cover lifts to shadowing orbit uniqueness, and introduces maps in Banach space related to shadowing orbits.

Contribution

It provides a new characterization of product Anosov diffeomorphisms using the two-sided limit shadowing property and develops a Banach space framework for shadowing orbits.

Findings

Anosov diffeomorphism is a product if and only if lifts have the unique two-sided limit shadowing property.

Introduces Banach space maps whose fixed points correspond to shadowing orbits.

Establishes a link between universal cover properties and shadowing orbit uniqueness.

Abstract

We characterize product Anosov diffeomorphisms in terms of the two-sided limit shadowing property. It is proved that an Anosov diffeomorphism is a product Anosov diffeomorphism if and only if any lift to the universal covering has the unique two-sided limit shadowing property. Then we introduce two maps in a suitable Banach space such that fixed points of these maps are related with shadowing orbits on the universal covering.