Ergodic components of partially hyperbolic systems

TL;DR

This paper classifies ergodic decompositions for certain volume-preserving partially hyperbolic systems, revealing structure of accessibility classes and extending results to non-volume-preserving cases.

Contribution

It provides a complete classification of ergodic decompositions for open families of partially hyperbolic diffeomorphisms, including systems with compact center leaves and perturbations of Anosov flows.

Findings

Non-open accessibility classes form a $C^1$ lamination

Results on accessibility classes of non-volume-preserving systems

Classification applies to systems with compact center leaves and Anosov flow perturbations

Abstract

This paper gives a complete classification of the possible ergodic decompositions for certain open families of volume-preserving partially hyperbolic diffeomorphisms. These families include systems with compact center leaves and perturbations of Anosov flows under conditions on the dimensions of the invariant subbundles. The paper further shows that the non-open accessibility classes form a $C^1$ lamination and gives results about the accessibility classes of non-volume-preserving systems. Note: this document has been modified slightly from earlier preprints. The numbering of sections was changed to match the published version and an erratum has been added to the end.