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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
Universitat de Vic. Escola Politècnica Superior; Universitat de Vic. Grup de Recerca en Tecnologies Digitals
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 .
Matemàtica
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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