Path formulation for multiparameter D3-equivariant bifurcation problems

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2010-11-22

Autores

Furter, Jacques-Élie
Sitta, Angela Maria [UNESP]

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Resumo

We implement a singularity theory approach, the path formulation, to classify D3-equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a Ba-miniversal unfolding f0 of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of F0 onto its unfolding parameter space. We apply our results to degenerate bifurcation of period-3 subharmonics in reversible systems, in particular in the 1:1-resonance.

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1:1-resonance, Degenerate bifurcation, Equivariant bifurcation, Path formulation, Reversible systems, Singularity theory, Subharmonic bifurcation

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Annales de l'Institut Fourier, v. 60, n. 4, p. 1363-1400, 2010.