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| Author(s): |
Otávio Marçal Leandro Gomide
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: | 2015-07-08 |
| Examining board members: |
Ricardo Miranda Martins;
Marco Antonio Teixeira;
João Carlos da Rocha Medrado
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| Advisor: | Ricardo Miranda Martins |
| Abstract | |
The study of minimal sets is a very active research topic in the qualitative theory of dynamical systems. In this master thesis we investigate the existence of limit cycles in smooth and non-smooth planar systems. In smooth dynamical systems, we present a formalization of averaging method and we use this tool to study the number of limit cycles in planar autonomous systems. As a result, we obtain a maximum number of limit cycles (detected by first order averaging) bifurcating from some classes of isochronous quadratic and cubic centers, through polynomial perturbations of degree n (for some values of n), and we conjecture the upper bound in the general case. Finally, we introduce the fascinating world of non-smooth dynamical systems, and we study the existence of crossing limit cycles in discontinuous planar piecewise linear systems which have a circle (S1) as discontinuity manifold. We exhibit configurations of saddle-center and focus-center cases which present a crossing limit cycle (AU) | |
| FAPESP's process: | 13/18168-5 - Non-smooth Dynamical Systems on the plane |
| Grantee: | Otávio Marçal Leandro Gomide |
| Support Opportunities: | Scholarships in Brazil - Master |