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Limit cycles in smooth and non-smooth dynamical systems

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Author(s):
Otávio Marçal Leandro Gomide
Total Authors: 1
Document type: Master's Dissertation
Press: Campinas, SP.
Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
Defense date:
Examining board members:
Ricardo Miranda Martins; Marco Antonio Teixeira; João Carlos da Rocha Medrado
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 type: Scholarships in Brazil - Master