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Journal of Modern Dynamics (JMD)
 

Partial hyperbolicity and ergodicity in dimension three

Pages: 187 - 208, Issue 2, April 2008      doi:10.3934/jmd.2008.2.187

 
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Federico Rodriguez Hertz - IMERL-Facultad de Ingeniería, Universidad de la República, ulio Herrera y Reissig 565, CC 30, 11300 Montevideo, Uruguay (email)
María Alejandra Rodriguez Hertz - IMERL-Facultad de Ingeniería, Universidad de la República, CC 30 Montevideo, Uruguay (email)
Raúl Ures - IMERL-Facultad de Ingeniería, Universidad de la República, CC 30 Montevideo, Uruguay (email)

Abstract: 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, accessibility property, ergodicity, laminations.
Mathematics Subject Classification:  Primary: 37D30, Secondary: 37A25.

Received: March 2007;      Revised: November 2007;      Available Online: January 2008.