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Title:
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Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2
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Author:
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Corbera Subirana, Montserrat; Llibre, Jaume; Pérez-Chavela, Ernesto
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Other authors:
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Universitat de Vic. Escola Politècnica Superior; Universitat de Vic. Grup de Recerca en Tecnologies Digitals |
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Notes:
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In this paper we consider vector fields in R3 that are invariant under a
suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two
singular points (e+ and e
−) and their invariant manifolds: one of dimension 2 (a sphere
minus the points e+ and e
−) and one of dimension 1 (the open diameter of the sphere
having endpoints e+ and e
−). In particular, we analyze the dynamics of the vector
field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove
the existence of infinitely many symmetric periodic orbits near L. We also study two
families of vector fields satisfying this dynamics. The first one is a class of quadratic
polynomial vector fields in R3, and the second one is the charged rhomboidal four body
problem. |
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Subject(s):
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-Matemàtica |
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Rights:
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(c) Institute of Physics
Tots els drets reservats
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Document type:
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Article
info:eu-repo/acceptedVersion |
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Published by:
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Institute of Physics
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