2008, 22(1&2): 75-88. doi: 10.3934/dcds.2008.22.75

Density of accessibility for partially hyperbolic diffeomorphisms with one-dimensional center

1. 

Department of Mathematics, Northwestern University, Evanston, IL 60208-2730, United States

2. 

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

3. 

IMERL-Facultad de Ingeniería, Universidad de la República, CC 30 Montevideo, Uruguay

Received  August 2007 Revised  February 2008 Published  June 2008

It is shown that stable accessibility property is $C^r$-dense among partially hyperbolic diffeomorphisms with one-dimensional center bundle, for $r \geq 2$, volume preserving or not. This establishes a conjecture by Pugh and Shub for these systems.
Citation: Keith Burns, Federico Rodriguez Hertz, María Alejandra Rodriguez Hertz, Anna Talitskaya, Raúl Ures. Density of accessibility for partially hyperbolic diffeomorphisms with one-dimensional center. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 75-88. doi: 10.3934/dcds.2008.22.75
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