Electron. J. Differential Equations, Vol. 2018 (2018), No. 118, pp. 1-14.

Limit cycles bifurcating from the periodic orbits of the weight-homogeneous polynomial centers of weight-degree 3

Jaume LLibre, Bruno D. Lopes, Jaime R. de Moraes

In this article we obtain two explicit polynomials, whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of polynomial differential centers of order 5, when this family is perturbed inside the class of all polynomial differential systems of order 5, whose average function of first order is not zero. Then the maximum number of limit cycles that bifurcate from these periodic orbits is 6 and it is reached. This family of of centers completes the study of the limit cycles which can bifurcate from periodic orbits of all centers of the weight-homogeneous polynomial differential systems of weight-degree 3 when perturbed in the class of all polynomial differential systems having the same degree and whose average function of first order is not zero.

Submitted November 16, 2016. Published May 17, 2018.
Math Subject Classifications: 34C07, 34C23, 34C25, 34C29, 37C10, 37C27, 37G15.
Key Words: Polynomial vector field; limit cycle; averaging method; weight-homogeneous differential system.

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Jaume LLibre
Departament de Matemàtiques
Universitat Autònoma de Barcelona
08193 Bellaterra, Barcelona
Catalonia, Spain
email: jllibre@mat.uab.cat
Bruno D. Lopes
Campinas, São Paulo, Brazil
email: brunodomicianolopes@gmail.com
Jaime R. de Moraes
Curso de Matemática - UEMS
Rodovia Dourados-Itaum Km 12
CEP 79804-970 Dourados
Mato Grosso do Sul, Brazil
email: jaime@uems.br

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