| Full text | |
| Author(s): |
Buzzi, Claudio A.
;
Rodero, Ana Livia
;
Teixeira, Marco A.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | PHYSICA D-NONLINEAR PHENOMENA; v. 440, p. 15-pg., 2022-08-08. |
| Abstract | |
In this article we discuss some qualitative and geometric aspects of non-smooth dynamical systems theory. Our main goal is to study stability problems inside the class of 3-dimensional refractive piecewise smooth vector fields. Our concern is to study refractive vector fields that admit a first integral that leaves invariant any sphere centered at the origin. Global stability conditions on generic one-parameter families of refractive piecewise smooth vector fields on a two-dimensional sphere are presented and used to prove our main result, which establishes necessary conditions for the structural stability inside that class.(c) 2022 Elsevier B.V. All rights reserved. (AU) | |
| FAPESP's process: | 18/13481-0 - Geometry of control, dynamical and stochastic systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |
| 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: | 19/00440-7 - Study of limit cycles in piecewise smooth systems on the sphere |
| Grantee: | Ana Livia Rodero |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 17/08779-8 - Thom-Smale Program for piecewise smooth differential systems in low dimensions manifolds |
| Grantee: | Ana Livia Rodero |
| Support Opportunities: | Scholarships in Brazil - Doctorate |