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Título:
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Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3
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Autor/a:
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Corbera Subirana, Montserrat; Llibre, Jaume
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Otros autores:
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Universitat de Vic. Escola Politècnica Superior; Universitat de Vic. Grup de Recerca en Tecnologies Digitals |
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Notas:
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In this paper we will find a continuous of periodic orbits passing
near infinity for a class of polynomial vector fields in R3. We consider
polynomial vector fields that are invariant under a symmetry with
respect to a plane and that possess a “generalized heteroclinic loop”
formed by two singular points e+ and e− at infinity and their invariant
manifolds � and . � is an invariant manifold of dimension 1 formed
by an orbit going from e− to e+, � is contained in R3 and is transversal
to . is an invariant manifold of dimension 2 at infinity. In fact, is
the 2–dimensional sphere at infinity in the Poincar´e compactification
minus the singular points e+ and e−. The main tool for proving the
existence of such periodic orbits is the construction of a Poincar´e map
along the generalized heteroclinic loop together with the symmetry
with respect to . |
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Materia(s):
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-Matemàtica |
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Derechos:
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Electronic version of an article published in International Journal of Bifurcation and Chaos, 2007, vol. 17, núm. 9, pàg. 3295-3302. http://dx.doi.org/10.1142/S0218127407019056 © World Scientific Publishing Company. http://www.worldscientific.com/doi/abs/10.1142/S0218127407019056?journalCode=ijbc
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Tipo de documento:
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Artículo
info:eu-repo/acceptedVersion |
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Editor:
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World Cientific Publishing
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Compartir:
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