Partial hyperbolicity and ergodicity in dimension three

F. Rodriguez Hertz, M. A. Rodriguez Hertz, R. Ures

Published 2006-11-25Version 1

In [15] the authors proved the Pugh-Shub conjecture for partially hyperbolic diffeomorphisms with 1-dimensional center, i.e. stable ergodic diffeomorphism are dense among the partially hyperbolic ones. In this work we address the issue of giving a more accurate description of this abundance of ergodicity. In particular, we give the first examples of manifolds in which all conservative partially hyperbolic diffeomorphisms are ergodic.