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

Partial hyperbolicity and ergodicity in dimension three

Federico Rodriguez Hertz 1, , María Alejandra Rodriguez Hertz 2, and  Raúl Ures 2,

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.
Keywords: partial hyperbolicity, laminations., accessibility property, ergodicity.
Mathematics Subject Classification: Primary: 37D30, Secondary: 37A2.
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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