Topologically transversal reversible homoclinic sets

Author:
Michal Feckan

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3369-3377

MSC (2000):
Primary 37C25, 37C29, 57R50

DOI:
https://doi.org/10.1090/S0002-9939-02-06473-0

Published electronically:
April 17, 2002

MathSciNet review:
1913016

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Abstract | References | Similar Articles | Additional Information

Abstract: An -reversible diffeomorphism on is studied possessing a hyperbolic fixed point. If the stable manifold of the hyperbolic fixed point and the fixed point set of have a nontrivial local topological crossing, then an infinite number of -symmetric periodic orbits of the diffeomorphism is shown. A perturbed problem is also studied by showing the relationship between a corresponding Melnikov function and the nontriviality of a local topological crossing of the set and the stable manifold for the perturbed diffeomorphism.

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Additional Information

**Michal Feckan**

Affiliation:
Department of Mathematical Analysis, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia

Email:
Michal.Feckan@fmph.uniba.sk

DOI:
https://doi.org/10.1090/S0002-9939-02-06473-0

Received by editor(s):
April 25, 2001

Received by editor(s) in revised form:
June 29, 2001

Published electronically:
April 17, 2002

Additional Notes:
The author was partially supported by Grant GA-MS 1/6179/00.

Communicated by:
Carmen Chicone

Article copyright:
© Copyright 2002
American Mathematical Society