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Singular perturbation problems for time-reversible systems
Author(s):
Claudio
A.
Buzzi;
Paulo
Ricardo
da Silva;
Marco
Antonio
Teixeira
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3323-3331.
MSC (2000):
Primary 34C14, 34C20, 34D15
Posted:
May 9, 2005
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Abstract:
In this paper singularly perturbed reversible vector fields defined in  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.
References:
-
- 1.
- F. Dumortier, R. Roussarie. Canard Cycles and Center Manifolds, Memoirs of the A.M.S, V. 121, 1996. MR 1327208 (96k:34113)
- 2.
- N. Fenichel. Geometric Singular Perturbation Theory for Ordinary Differential Equations, J.D.E 31, 53-98, 1979. MR 0524817 (80m:58032)
- 3.
- P. Szmolyan. Transversal Heteroclinic and Homoclinic Orbits in Singular Perturbation Problems , J.D.E 92, 252-281, 1991. MR 1120905 (92e:58185)
- 4.
- W. G. Hoover, H. A. Posch, B. L. Holian, M. J. Gillan, M. Mareshal and C. Massobrio. Dissipative irreversibility from Nosé's reversible mechanics, Mol. Simulation 1, 79-86, 1987.
- 5.
- J. S. W. Lamb and J. A. G. Roberts.
Time-reversal symmetry in dynamical systems: a survey.
Phys. D, 112(1-2):1-39, 1998.
Time-reversal symmetry in dynamical systems (Coventry, 1996). MR 1605826 (99b:58174) - 6.
- M. Krupa and P. Szmolyan. Extending geometric singular perturbation theory to nonhyperbolic points: fold and Canard points in two dimensions, SIAM J. Math. Anal. 33, 2, 286-314, 2001. MR 1857972 (2002g:34117)
- 7.
- M. Krupa and P. Szmolyan. Extending slow manifolds near transcritical and pitchfork singularities, Nonlinearity 14, 1473-1491, 2001. MR 1867088 (2002k:34112)
- 8.
- J. A. G. Roberts and G. R. W. Quispel.
Chaos and time-reversal symmetry. Order and chaos in reversible dynamical systems.
Phys. Rep., 216(2-3):63-177, 1992. MR 1173588 (94a:58135)
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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 Cienti\~fica, Universidade Estadual de Campinas, Campinas, SP, CEP 13081-970, Brazil
Email:
teixeira@ime.unicamp.br
DOI:
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.
Posted:
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
Copyright of article:
Copyright
2005,
American Mathematical Society
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