Notes on regularity of Anosov splitting

TL;DR

This paper provides a proof of the regularity of Anosov splitting for Anosov diffeomorphisms on tori and extends the approach to higher dimensions and flows, enhancing understanding of hyperbolic dynamics.

Contribution

It offers a new proof of Anosov splitting regularity and generalizes the concept to higher-dimensional systems and flows.

Findings

Proof of regularity of Anosov splitting on tori

Extension of regularity results to higher dimensions

Application to Anosov flows

Abstract

In these expository notes, we give a proof of regularity of Anosov splitting for Anosov diffeomorphisms in a torus. We also generalize the idea to higher dimensions and to Anosov flows.