| Full text | |
| Author(s): |
Carvalho, Tiago
;
Cunha, Jackson
;
Perez, Otavio Henrique
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 453, p. 36-pg., 2025-11-03. |
| Abstract | |
In this paper we are dealing with planar piecewise smooth vector fields defined in two zones. In each one of such zones takes place a smooth vector field and the switching manifold is a curve passing through the origin. The first one of these smooth vector fields has a saddle-node equilibrium at the origin, while the second one is transversal to the switching manifold at the origin. We will consider a singular perturbation of this scenario, involving a non-hyperbolic equilibrium considered over the switching manifold. With this purpose, we regularize the piecewise smooth vector field using the Sotomayor-Teixeira method. After it, the singular perturbation theory is considered and a unique non-normally hyperbolic point is obtained and a sequence of blow-ups is considered in order to completely desingularize this point and understand the dynamics around it. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU) | |
| FAPESP's process: | 22/02819-6 - Intermittent vector fields: theoretical aspects and applications |
| Grantee: | Tiago de Carvalho |
| Support Opportunities: | Research Grants - Initial Project |
| FAPESP's process: | 21/10198-9 - Invariant manifolds and limit periodic sets of discontinuous foliations |
| Grantee: | Otavio Henrique Perez |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 19/10269-3 - Ergodic and qualitative theories of dynamical systems II |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 21/12395-6 - Piecewise smooth vector fields: theory and applications |
| Grantee: | Tiago de Carvalho |
| Support Opportunities: | Regular Research Grants |