Geometric Singular Perturbation Theory for Systems with Symmetry

• Autor(a) principal: Cardin, Pedro Toniol [UNESP]
• Data de Publicação: 2020
• Outros Autores: Teixeira, Marco Antonio
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1007/s10884-020-09855-2; http://hdl.handle.net/11449/198962
• topic: Fast-slow systems; Reversible vector fields; Symmetries

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 ε 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 ε→ 0 in the fast and slow time scales. This approach is applied to a number of examples.