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Anais da Academia Brasileira de Ciências

versão impressa ISSN 0001-3765versão On-line ISSN 1678-2690

Resumo

MESSIAS, MARCELO. Periodic perturbations of quadratic planar polynomial vector fields. An. Acad. Bras. Ciênc. [online]. 2002, vol.74, n.2, pp.193-198. ISSN 0001-3765.  http://dx.doi.org/10.1590/S0001-37652002000200001.

In this work are studied periodic perturbations, depending on two parameters, of quadratic planar polynomial vector fields having an infinite heteroclinic cycle, which is an unbounded solution joining two saddle points at infinity. The global study envolving infinity is performed via the Poincaré compactification. The main result obtained states that for certain types of periodic perturbations, the perturbed system has quadratic heteroclinic tangencies and transverse intersections between the local stable and unstable manifolds of the hyperbolic periodic orbits at infinity. It implies, via the Birkhoff-Smale Theorem, in a complex dynamical behavior of the solutions of the perturbed system, in a finite part of the phase plane.

Palavras-chave : heteroclinic cycles; periodic perturbations; polynomial systems.

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