| Full text | |
| Author(s): |
Lamb, Jeroen S. W.
;
Teixeira, Marco Antonio
;
Webster, Kevin N.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 219, n. 1, p. 78-115, Dec. 2005. |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics |
| Abstract | |
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) | |
| FAPESP's process: | 02/10246-2 - Control systems, dynamical systems, stochastic dynamical systems, Lie theory and differential geometry |
| Grantee: | Luiz Antonio Barrera San Martin |
| Support Opportunities: | Research Projects - Thematic Grants |