Jaume LLibre, Bruno D. Lopes, Jaime R. de Moraes
Abstract:
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 |
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Bruno D. Lopes IMECC--UNICAMP, CEP 13081-970 Campinas, São Paulo, Brazil email: brunodomicianolopes@gmail.com |
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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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