On spiral periodic points and saddles for surface diffeomorphisms

C. Morales

doi:10.3934/dcds.2011.29.1191

Article Contents

2011, Volume 29, Issue 3: 1191-1195. Doi: 10.3934/dcds.2011.29.1191

This issue Previous Article Computational hyperbolicity Next Article Stable transitivity for extensions of hyperbolic systems by semidirect products of compact and nilpotent Lie groups

On spiral periodic points and saddles for surface diffeomorphisms

C. Morales^1,

1.
Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970, Rio de Janeiro

Received: January 31, 2010

Revised: May 31, 2010

Published: August 2011

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Abstract

We prove that a $C^1$ generic orientation-preserving diffeomorphism of a closed orientable surface either is Axiom A without cycles or the closures of the sets of saddles and of periodic points without real eigenvalues have nonempty intersection.

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Mathematics Subject Classification: Primary: 37D30; Secondary: 37D45.

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