Robustly expansive homoclinic classes are generically hyperbolic

Martín Sambarino; José L. Vieitez

doi:10.3934/dcds.2009.24.1325

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2009, Volume 24, Issue 4: 1325-1333. Doi: 10.3934/dcds.2009.24.1325

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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

Received: June 30, 2008

Revised: October 31, 2008

Published: October 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 37D30; Secondary: 37D20,37C29.

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