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

 

Singular perturbation problems for time-reversible systems


Authors: Claudio A. Buzzi, Paulo Ricardo da Silva and Marco Antonio Teixeira
Journal: Proc. Amer. Math. Soc. 133 (2005), 3323-3331
MSC (2000): Primary 34C14, 34C20, 34D15
Published electronically: May 9, 2005
MathSciNet review: 2161156
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Abstract: In this paper singularly perturbed reversible vector fields defined in $R^n$ without normal hyperbolicity conditions are discussed. The main results give conditions for the existence of infinitely many periodic orbits and heteroclinic cycles converging to singular orbits with respect to the Hausdorff distance.


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Additional Information

Claudio A. Buzzi
Affiliation: IBILCE, Universidade Estadual Paulista, São José do Rio Preto, SP, CEP 15054-000, Brazil
Email: buzzi@mat.ibilce.unesp.br

Paulo Ricardo da Silva
Affiliation: IBILCE, Universidade Estadual Paulista, São José do Rio Preto, SP, CEP 15054-000, Brazil
Email: prs@mat.ibilce.unesp.br

Marco Antonio Teixeira
Affiliation: Instituto de Matemática, Estatística e Computação Cientıfica, Universidade Estadual de Campinas, Campinas, SP, CEP 13081-970, Brazil
Email: teixeira@ime.unicamp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07894-9
PII: S 0002-9939(05)07894-9
Keywords: Singular perturbations, time-reversible systems
Received by editor(s): March 4, 2004
Received by editor(s) in revised form: June 21, 2004
Published electronically: May 9, 2005
Additional Notes: The first author was partially supported by CAPES 0092/01-0.
The second author was partially supported by CAPES 0092/01-0 and CNPq 476886/2001-5
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2005 American Mathematical Society