# Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center

## TL;DR

This paper investigates transitive partially hyperbolic diffeomorphisms with a one-dimensional neutral center, establishing the existence of an invariant metric along the center foliation and classifying such systems on 3-manifolds.

## Contribution

It introduces the concept of topologically neutral centers in partially hyperbolic systems and provides a classification for these systems on 3-manifolds.

## Key findings

- Existence of a continuous invariant metric along the center foliation.
- Classification of transitive partially hyperbolic diffeomorphisms with neutral center on 3-manifolds.
- Systems are dynamically coherent.

## Abstract

In this paper, we study transitive partially hyperbolic diffeomorphisms with one-dimensional topologically neutral center, meaning that the length of the iterate of small center segments remains small. Such systems are dynamically coherent. We show that there exists a continuous metric along the center foliation which is invariant under the dynamics. As an application, we classify the transitive partially hyperbolic diffeomorphisms on 3-manifolds with topologically neutral center.