Center bunching without dynamical coherence

TL;DR

This paper constructs examples of volume-preserving partially hyperbolic diffeomorphisms that are accessible and center bunched but lack dynamical coherence, and shows isotopy results related to Anosov systems.

Contribution

It provides the first known examples of non-dynamically coherent, center bunched, accessible partially hyperbolic diffeomorphisms in the volume-preserving setting.

Findings

Existence of open families of such diffeomorphisms

Construction of non-Anosov examples isotopic to Anosov diffeomorphisms

Clarification of the relationship between partial hyperbolicity and Anosov systems

Abstract

We answer a question of Burns and Wilkinson, showing that there are open families of volume-preserving partially hyperbolic diffeomorphisms which are accessible and center bunched and neither dynamically coherent nor Anosov. We also show in the volume-preserving setting that any diffeomorphism which is partially hyperbolic and Anosov may be isotoped to a diffeomorphism which is partially hyperbolic and not Anosov.