On the Limit Cycles of a Class of Discontinuous Piecewise Differential Systems Formed by Two Rigid Centers Governed by Odd Degree Polynomials

Author:

Carvalho Tiago1,Gonçalves Luiz Fernando2,Llibre Jaume3

Affiliation:

1. Departamento de Computação e Matemática, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Av. Bandeirantes, 3900, 14040-901, Ribeirão Preto, SP, Brazil

2. Instituto de Matemática e Estatística, Universidade Federal de Goiás, Campus Samambaia, CEP 74690-900, Goiânia, GO, Brazil

3. Departament de Matemàtiques, Facultat de Ciències, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain

Abstract

We provide an upper bound for the maximum number of limit cycles for the class of discontinuous piecewise differential systems formed by two differential systems separated by the straight line [Formula: see text], one of which is a linear rigid center while the other is a rigid center formed of a linear part plus a homogeneous polynomial of odd degree. We solve the extended 16th Hilbert problem for this class of discontinuous piecewise differential systems.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

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