# Structure of accessibility classes

## TL;DR

This paper investigates the structure of accessibility classes in partially hyperbolic diffeomorphisms with two-dimensional central directions, establishing conditions under which these classes are immersed manifolds with specific smoothness properties.

## Contribution

It proves that accessibility classes are immersed manifolds and, under additional conditions, are $C^{1}$ immersed manifolds, advancing understanding of their geometric structure.

## Key findings

- Accessibility classes are immersed manifolds in general.
- Under certain bunching and coherence conditions, classes are $C^{1}$ immersed.
- Provides new insights into the smoothness and structure of accessibility classes.

## Abstract

In this work we deal with partially hyperbolic diffeomorphisms whose central direction is two dimensional. We prove that in general the accessibility classes are immersed manifolds. If, furthermore, the diffeomorphism is dynamically coherent and satisfies certain bunching condition, then the accessibility classes are $C^{1}$ immersed manifolds.