Cardin, Pedro Toniol [UNESP]Teixeira, Marco Antonio2020-12-122020-12-122020-01-01Journal of Dynamics and Differential Equations.1572-92221040-7294http://hdl.handle.net/11449/198962In 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.engFast-slow systemsReversible vector fieldsSymmetriesArtigo10.1007/s10884-020-09855-22-s2.0-85086154075