Quasi-isometric center action in dimension 3

TL;DR

This paper investigates certain 3D dynamical systems that preserve a center foliation and act quasi-isometrically, demonstrating they are essentially skew-products or discretized Anosov flows after finite modifications.

Contribution

It classifies transitive partially hyperbolic diffeomorphisms in dimension 3 with quasi-isometric center foliation as either skew-products or discretized Anosov flows, up to finite lift and iterate.

Findings

Diffeomorphisms are either skew-products or discretized Anosov flows.

Classification holds after finite lift and iteration.

Provides a structural understanding of 3D partially hyperbolic systems.

Abstract

We study transitive partially hyperbolic diffeomorphisms in dimension 3 preserving a center foliation on which they act quasi-isometrically. We show that the diffeomorphism is up to finite lift and iterate, either a skew-product or a discretised Anosov flow.