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| Author(s): |
Ana Livia Rodero
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São José do Rio Preto. 2022-03-03. |
| Institution: | Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto |
| Defense date: | 2022-02-03 |
| Advisor: | Claudio Aguinaldo Buzzi; Joan Torregrosa |
| Abstract | |
The first goal of this work was to study structural stability problems in the classes of piecewise smooth and piecewise smooth refractive vector fields that admit a first integral that leaves invariant any two-dimensional sphere centered at the origin. Stability conditions and generic one-parameter families in the two-dimensional sphere were used to prove the results that establish the necessary conditions for structural stability in these classes. Furthermore, we study the center-focus and the cyclicity problems in the classes of smooth and piecewise smooth vector fields that admit a first integral that leaves invariant any two-dimensional spheres centered at the origin. We prove that linear systems into these classes do not admit limit cycle on invariant spheres. Finally, we obtain 4 small amplitude limit cycles bifurcating from a weak-focus of a (smooth) quadratic system defined on the unit sphere and we also show that there exists a piecewise smooth quadratic perturbation such that at least 10 small amplitude limit cycles bifurcate from a smooth quadratic center on this sphere. (AU) | |
| 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 |