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Limit cycles for piecewise smooth dynamical systems in dimension n>2 and in compact manifolds

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Author(s):
Joyce Aparecida Casimiro
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; Gabriel Ponce; Luis Fernando de Osorio Mello
Advisor: Ricardo Miranda Martins
Abstract

The study of minimal sets helps to comprehend the global qualitative behaviour of dynamical systems. In this way, to determine the existence or not of such sets is an important and widely studied topic in this area. In this dissertation we investigate whether a vector field possessing a compact manifold filled by periodic orbits admits limit cycles after a small perturbation. Besides the existence of limit cycles, we obtain an upper bound for the number of limit cycles and, in some cases, we proved that this upper bound is attained. The main tool employed to obtain these results was the Averaging Theory. Two types of systems were considered: the smooth and the non-smooth ones, where for the latter type of systems, we used Filipov's Convention (AU)

FAPESP's process: 17/04689-4 - Limit cycles for piecewise smooth dynamical systems in dimension n>2 and in compact manifolds
Grantee:Joyce Aparecida Casimiro
Support type: Scholarships in Brazil - Master