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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Another dichotomy for surface diffeomorphisms


Author: C. Morales
Journal: Proc. Amer. Math. Soc. 137 (2009), 2639-2644
MSC (2000): Primary 37D30; Secondary 37E30
Published electronically: March 27, 2009
MathSciNet review: 2497476
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Abstract: We prove that a $ C^1$ generic orientation-preserving diffeomorphism of a closed orientable surface either has infinitely many periodic points with complex (nonreal) eigenvalues or is Axiom A without cycles. This improves Mañé's dichotomy.


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Additional Information

C. Morales
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, 21945-970, Rio de Janeiro, RJ, Brazil
Email: morales@impa.br

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09879-7
PII: S 0002-9939(09)09879-7
Keywords: Axiom A diffeomorphism, homoclinic tangency, complex eigenvalues
Received by editor(s): August 18, 2008
Published electronically: March 27, 2009
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2009 American Mathematical Society