| Texto completo | |
| Autor(es): |
Lamb, Jeroen S. W.
;
Teixeira, Marco Antonio
;
Webster, Kevin N.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Differential Equations; v. 219, n. 1, p. 78-115, Dec. 2005. |
| Área do conhecimento: | Ciências Exatas e da Terra - Matemática |
| Assunto(s): | Sistemas dinâmicos Simetria |
| Resumo | |
We study the dynamics near a symmetric Hopf-zero (also known as saddle-node Hopf or fold-Hopf) bifurcation in a reversible vector field in R-3, with involutory an reversing symmetry whose fixed point subspace is one-dimensional. We focus on the case in which the normal form for this bifurcation displays a degenerate family of heteroclinics between two asymmetric saddle-foci. We study local perturbations of this degenerate family of heteroclinics within the class of reversible vector fields and establish the generic existence of hyperbolic basic sets (horseshoes), independent of the eigenvalues of the saddle-foci, as well as cascades of bifurcations of periodic, heteroclinic and homoclinic orbits. (AU) | |
| Processo FAPESP: | 02/10246-2 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos |
| Beneficiário: | Luiz Antonio Barrera San Martin |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |