Electron. J. Diff. Equ., Vol. 2015 (2015), No. 271, pp. 1-8.

Limit cycles bifurcating from the periodic annulus of cubic homogeneous polynomial centers

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

We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of any cubic homogeneous polynomial center when it is perturbed inside the class of all polynomial differential systems of degree n.

Submitted October 8, 2014. Published October 21, 2015.
Math Subject Classifications: 37C10, 34H99.
Key Words: Polinomial vector field; limit cycle; averaging method; periodic orbit; isochronous center; homogeneous cubic centers.

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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
Departamento de Matemática - IBILCE-UNESP
Rua C. Colombo, 2265, CEP 15054-000
S. J. Rio Preto, 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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