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Another dichotomy for surface diffeomorphisms
Author(s):
C.
Morales
Journal:
Proc. Amer. Math. Soc.
137
(2009),
2639-2644.
MSC (2000):
Primary 37D30;
Secondary 37E30
Posted:
March 27, 2009
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Abstract:
We prove that a  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:
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
Posted:
March 27, 2009
Communicated by:
Jane M. Hawkins
Copyright of article:
Copyright
2009,
American Mathematical Society
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