Symmetric periodic orbits near a heteroclinic loop in R-3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

Autor(es)

Corbera, Montserrat ^[1] ; Llibre, Jaume ^[2] ; Antonio Teixeira, Marco ^[3]

Afiliação do(s) autor(es)

^[1] Univ Vic, Dept Tecnol Digitals & Informac, Barcelona 08500, Catalonia - Spain

^[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia - Spain

^[3] Univ Estadual Campinas, Dept Matemat, BR-13083970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA D-NONLINEAR PHENOMENA; v. 238, n. 6, p. 699-705, APR 1 2009.
• Citações Web of Science: 6

Resumo

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. (AU)

• Processo FAPESP: 07/06896-5 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Luiz Antonio Barrera San Martin
• Modalidade de apoio: Auxílio à Pesquisa - Temático