Accessibility for dynamically coherent partially hyperbolic diffeomorphisms with 2D center

TL;DR

This paper demonstrates that within a specific class of partially hyperbolic diffeomorphisms with 2D centers, stable accessibility is densely achievable through small perturbations, under certain conditions.

Contribution

It proves that stable accessibility is $C^r$-dense among these diffeomorphisms, extending understanding of accessibility in partially hyperbolic systems.

Findings

Stable accessibility is $C^r$-dense for these systems.

The result applies to systems satisfying strong bunching and stable dynamical coherence.

Density holds for all integer $r \, \geq 2$.

Abstract

We show that for any integer $r \geq 2$, stable accessibility is $C^r$-dense among partially hyperbolic diffeomorphisms with two-dimensional center that satisfy some strong bunching and are stably dynamically coherent.