| Full text | |
| Author(s): |
Perez, Otavio Henrique
;
da Silva, Paulo Ricardo
Total Authors: 2
|
| Document type: | Journal article |
| Source: | SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES; v. N/A, p. 26-pg., 2024-06-24. |
| Abstract | |
The main goal of this paper is to study compactifications of polynomial slow-fast systems. More precisely, the aim is to give conditions in order to guarantee normal hyperbolicity at infinity of the Poincar & eacute;-Lyapunov sphere for slow-fast systems defined in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}<^>{n}$$\end{document}. For the planar case, we prove a global version of the Fenichel Theorem, which assures the persistence of invariant manifolds in the whole Poincar & eacute;-Lyapunov disk. We also discuss the occurrence of non normally hyperbolic points at infinity, namely: fold, transcritical and pitchfork singularities. (AU) | |
| FAPESP's process: | 23/02959-5 - Non-Smooth Systems and Singular Perturbations |
| Grantee: | Paulo Ricardo da Silva |
| Support Opportunities: | Regular Research Grants |
| 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 |