Some Remarks on Anosov Families

TL;DR

This paper investigates specific classes of Anosov families, demonstrating their canonical coordinates, expansiveness, shadowing property, and existence of Markov partitions, thus advancing understanding of their dynamical structure.

Contribution

It proves that a particular class of Anosov families admits canonical coordinates, are expansive, satisfy shadowing, and have Markov partitions, providing new insights into their structure.

Findings

Existence of canonical coordinates for certain Anosov families

Anosov families are expansive

They satisfy the shadowing property and have Markov partitions

Abstract

We study Anosov families which are sequences of diffeomorphisms along compact Riemannian manifolds such that the tangent bundle split into expanding and contracting subspaces. In this paper we prove that a certain class of Anosov families: (i) admit canonical coordinates (ii) are expansive, (iii) satisfy the shadowing property, and (iv) exhibit a Markov partition.