Invariant manifolds and limit periodic sets of discontinuous foliations
| Full text | |
| Author(s): |
Cardin, Pedro Toniol
;
Teixeira, Marco Antonio
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Dynamics and Differential Equations; v. 34, n. 2, p. 13-pg., 2020-06-08. |
| Abstract | |
In this paper we focus on a class of symmetric vector fields in the context of singularly perturbed fast-slow dynamical systems. Our main question is to know how symmetry properties of a dynamical system are affected by singular perturbations. In addition, our approach uses tools in geometric singular perturbation theory [8], which address the persistence of normally hyperbolic compact manifolds. We analyse the persistence of such symmetry properties when the singular perturbation parameter e is positive and small enough, and study the existing relations between symmetries of the singularly perturbed system and symmetries of the limiting systems, which are obtained from the limit epsilon -> 0 in the fast and slow time scales. This approach is applied to a number of examples. (AU) | |
| FAPESP's process: | 19/00976-4 - Dynamical systems with multiple time scales |
| Grantee: | Pedro Toniol Cardin |
| Support Opportunities: | Regular Research Grants |