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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: An $R$-reversible diffeomorphism on $\mathbb{R}^{2N}$ is studied possessing a hyperbolic fixed point. If the stable manifold of the hyperbolic fixed point and the fixed point set ${Fix}\, R$ of $R$ have a nontrivial local topological crossing, then an infinite number of $R$-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 ${Fix}\, R$ 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

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