Partial hyperbolicity and ergodicity in dimension three

Details Partial hyperbolicity and ergodicity in dimension three Partial hyperbolicity and ergodicity in dimension three

2006-11-25

arxiv.org/abs/math/0611787v1

Mathematics

Dynamical Systems

14 pages

Scientific paper

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.

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