# Classification of partially hyperbolic diffeomorphisms under some rigid conditions

## TL;DR

This paper classifies three-dimensional partially hyperbolic diffeomorphisms under specific rigid conditions, showing they are essentially either Anosov, skew-products, or time-one maps of Anosov flows, confirming a known conjecture in this setting.

## Contribution

It proves a classification result for partially hyperbolic diffeomorphisms under certain rigid tangent bundle conditions, extending the understanding of their structure.

## Key findings

- Diffeomorphisms are classified as Anosov, skew-products, or time-one maps of Anosov flows
- The classification confirms a conjecture for a restricted class of systems
- The results rely on rigid hypotheses on tangent bundle dynamics

## Abstract

Consider a three dimensional partially hyperbolic diffeomorphism. It is proven that under some rigid hypothesis on the tangent bundle dynamics, the map is (modulo finite covers and iterates) either an Anosov diffeomorphism, a skew-product or the time-one map of an Anosov flow, thus recovering a well known classification conjecture of the second author to this restricted setting.