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Symmetric periodic orbits near heteroclinic loops at infinity for a class of polynomial vector fields
Universitat de Vic. Escola Politècnica Superior; Universitat de Vic. Grup de Recerca en Tecnologies Digitals
For polynomial vector fields in R3, in general, it is very difficult to detect the existence of an open set of periodic orbits in their phase portraits. Here, we characterize a class of polynomial vector fields of arbitrary even degree having an open set of periodic orbits. The main two tools for proving this result are, first, the existence in the phase portrait of a symmetry with respect to a plane and, second, the existence of two symmetric heteroclinic loops.
Electronic version of an article published as International Journal of Bifurcation and Chaos, 2006, vol. 16, núm. 11, pàg. 3401-3410. [10.1142/S0218127406016884] © [copyright World Scientific Publishing Company] []
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