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| Author(s): |
Luan Vinicio de Mattos Ferreira Silva
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2019-02-28 |
| Examining board members: |
Douglas Duarte Novaes;
Ricardo Miranda Martins;
Paulo Ricardo da Silva
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| Advisor: | Douglas Duarte Novaes |
| Abstract | |
In this work, we performed a qualitative study of some global aspects of Filippov systems. By using methods from the qualitative theory of smooth dynamical systems, we addressed problems related to the persistence of minimal sets (limit cycles, invariant tori, etc) and to the asymptotic behavior of the solutions. Firstly, we used the Lyapunov criterion to study conditions in which the solutions of a particular family of defferential inclusions are all unbounded. Subsequently, considering a family of second order discontinuous differential equations, F, we established transformations in order to make feasible the use of some tools of the KAM Theory. Such tools ensure the existence of infinitely many invariant tori and periodic solutions, as well as they ensure results on the asymptotic behavior of solutions. Finally, we used the Melnilkov Method to obtain partial results on the existence of limit cycles for differential equations in F (AU) | |
| FAPESP's process: | 16/25459-4 - Persistence of minimal sets in dynamic systems |
| Grantee: | Luan Vinicio de Mattos Ferreira Silva |
| Support Opportunities: | Scholarships in Brazil - Master |