Ergodic components of partially hyperbolic systems

Andy Hammerlindl

Published 2014-09-29Version 1

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 the condition that the unstable and center bundles are one-dimensional. 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.