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November  2009, 24(4): 1325-1333. doi: 10.3934/dcds.2009.24.1325

Robustly expansive homoclinic classes are generically hyperbolic

Martín Sambarino 1, and  José L. Vieitez 2,

1. 

Facultad de Ciencias, Iguá 4225 y Mataojo, Universidad de la República, Montevideo
2. 

Facultad deIngeniería, Herrera y Reissig 565, Universidad de la República, Montevideo, Uruguay

Received  July 2008 Revised  November 2008 Published  May 2009

Let $f: M \to M$ be a diffeomorphism defined in a $d$-dimensional compact boundary-less manifold $M$. We prove that generically $C^1$-robustly expansive homoclinic classes $H(p)$, $p$ an $f$-hyperbolic periodic point, are hyperbolic.
Keywords: Dominated Splitting, Hyperbolicity, Expansiveness, Homoclinic Classes..
Mathematics Subject Classification: Primary: 37D30; Secondary: 37D20,37C2.
Citation: Martín Sambarino, José L. Vieitez. Robustly expansive homoclinic classes are generically hyperbolic. Discrete & Continuous Dynamical Systems - A, 2009, 24 (4) : 1325-1333. doi: 10.3934/dcds.2009.24.1325
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