Publication: Resonances and subharmonic bifurcations of large amplitude periodic orbits of planar polynomial vector fields
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World Scientific Publ Co Pte Ltd
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Abstract
In this work are studied periodic perturbations, depending on two parameters, of planar polynomial vector fields having an annulus of large amplitude periodic orbits, which accumulate on a symmetric infinite heteroclinic cycle. Such periodic orbits and the heteroclinic trajectory can be seen only by the global consideration of the polynomial vector fields on the whole plane, and not by their restriction to any compact set. The global study involving infinity is performed via the Poincare Compactification. It is shown that, for certain types of periodic perturbations, one can seek, in a neighborhood of the origin in the parameter plane, curves C-(m) of subharmonic bifurcations, for which the periodically perturbed system has subharmonics of order m, for any integer m.
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English
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Equadiff 2003: International Conference on Differential Equations. Singapore: World Scientific Publ Co Pte Ltd, p. 880-885, 2005.
