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Type: Artigo de periódico
Title: Symmetric periodic orbits near a heteroclinic loop in R-3 formed by two singular points, a semistable periodic orbit and their invariant manifolds
Author: Corbera, M
Llibre, J
Teixeira, MA
Abstract: In this paper, we consider C-1 vector fields X in R-3 having a "generalized heteroclinic loop" L which is topologically homeomorphic to the union of a 2-dimensional sphere S-2 and a diameter Gamma connecting the north with the south pole. The north pole is an attractor on S-2 and a repeller on Gamma. The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S-2. We also assume that the flow of X is invariant Under a topological straight line symmetry on the equator plane of the ball. For each n is an element of N, by means of a convenient Poincare map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around X in a period. We also exhibit a class of polynomial vector fields of degree 4 in R-3 satisfying this dynamics. (C) 2009 Elsevier B.V. All rights reserved.
Subject: Heteroclinic loop
Symmetric periodic orbits
Polynomial vector fields
Country: Holanda
Editor: Elsevier Science Bv
Citation: Physica D-nonlinear Phenomena. Elsevier Science Bv, v. 238, n. 6, n. 699, n. 705, 2009.
Rights: fechado
Identifier DOI: 10.1016/j.physd.2009.01.002
Date Issue: 2009
Appears in Collections:Unicamp - Artigos e Outros Documentos

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