# American Institute of Mathematical Sciences

April  2008, 2(2): 187-208. doi: 10.3934/jmd.2008.2.187

## Partial hyperbolicity and ergodicity in dimension three

 1 IMERL-Facultad de Ingeniería, Universidad de la República, ulio Herrera y Reissig 565, CC 30, 11300 Montevideo, Uruguay 2 IMERL-Facultad de Ingeniería, Universidad de la República, CC 30 Montevideo, Uruguay, Uruguay

Received  March 2007 Revised  November 2007 Published  January 2008

In [15] the authors proved the Pugh–Shub conjecture for partially hyperbolic diffeomorphisms with 1-dimensional center, i.e., stably ergodic diffeomorphisms 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.
Citation: Federico Rodriguez Hertz, María Alejandra Rodriguez Hertz, Raúl Ures. Partial hyperbolicity and ergodicity in dimension three. Journal of Modern Dynamics, 2008, 2 (2) : 187-208. doi: 10.3934/jmd.2008.2.187
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