Chain-transitivity of partially hyperbolic diffeomorphisms on $\mathbb{T}^3$ isotopic to Anosov

TL;DR

This paper proves that any partially hyperbolic diffeomorphism on the 3-torus, which is isotopic to an Anosov diffeomorphism, exhibits chain transitivity, indicating a form of topological mixing.

Contribution

It establishes the chain transitivity of partially hyperbolic diffeomorphisms on -torus isotopic to Anosov, extending understanding of their dynamical properties.

Findings

All such diffeomorphisms are chain transitive.

The result applies to diffeomorphisms isotopic to Anosov on -torus.

It advances the classification of dynamical behaviors on -torus.

Abstract

We prove that if $f$ is a partially hyperbolic diffeomorphism on 3-torus $\mathbb{T}^3$ and isotopic to Anosov, then $f$ is chain transitive.