Accessibility of derived-from-Anosov systems

TL;DR

This paper proves that any non-Anosov partially hyperbolic diffeomorphism on the 3-torus homotopic to Anosov systems must be accessible, contributing to the understanding of dynamical properties of such systems.

Contribution

It establishes a new result linking non-Anosov partial hyperbolicity and accessibility on the 3-torus, expanding the classification of these dynamical systems.

Findings

Non-Anosov partially hyperbolic diffeomorphisms on the 3-torus homotopic to Anosov are necessarily accessible.

The result narrows the possible behaviors of such systems, aiding in their classification.

Provides insights into the structure of partially hyperbolic systems on the 3-torus.

Abstract

This paper shows any non-Anosov partially hyperbolic diffeomorphism on the 3-torus which is homotopic to Anosov must be accessible.