Transitivity of conservative diffeomorphisms isotopic to Anosov on $\mathbb{T}^3$

TL;DR

This paper proves that certain volume-preserving diffeomorphisms on the 3-torus, which are close to linear Anosov automorphisms, are transitive, extending understanding of dynamical behavior in partially hyperbolic systems.

Contribution

It establishes transitivity for volume-preserving $C^{1+}$ diffeomorphisms isotopic to Anosov automorphisms on $ op^3$ along weakly partially hyperbolic paths.

Findings

Transitivity holds for volume-preserving $C^{1+}$ diffeomorphisms on $ op^3$.

Results extend to systems isotopic to linear Anosov automorphisms.

Supports broader understanding of dynamics in partially hyperbolic systems.

Abstract

We prove transitivity for volume preserving $C^{1+}$ diffeomorphisms on $\mathbb{T}^3$ which are isotopic to a linear Anosov automorphism along a path of weakly partially hyperbolic diffeomorphisms.