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| Author(s): |
Yagor Romano Carvalho
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São José do Rio Preto. 2021-03-03. |
| Institution: | Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto |
| Defense date: | 2021-01-27 |
| Advisor: | Claudio Aguinaldo Buzzi; Armengol Gasull |
| Abstract | |
In this work we are interested in some topics and problems about the qualitative theory of differential systems. We analyzed some bifurcations in a class of piecewise smooth systems with singular borders via regularization. We study lower bound for the number of limit cycles in a class of planar systems given by the perturbation of a linear center by a sum of homogeneous continuous vector fields, and we applied them in models that lose their smoothness at singular borders. A variant of Hilbert 16th problem is proposed, in order to bound the number of limit cycles in terms of the number of monomials in a family of polynomial vector fields. We investigated higher bound for the maximum number of crossing limit cycles, in a class of piecewise smooth systems separated by a straight line having combinations of linear centers and cubic isochronous centers with homogeneous non-linearity, showing some concrete examples that reach some higher bounds. We developed a procedure to calculate the Taylor expansion, in terms of energy levels, of the period function for a non-degenerate center, for any analytic Hamiltonian system and we apply it to several examples, being possible, in one of them, to study the number of limit cycles bifurcating from an Abelian integral. (AU) | |
| FAPESP's process: | 16/00242-2 - Bifurcation of piecewise smooth systems with singular borders via regularization |
| Grantee: | Yagor Romano Carvalho |
| Support Opportunities: | Scholarships in Brazil - Doctorate |