Robustly expansive homoclinic classes are generically hyperbolic

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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

Abstract
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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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