Bifurcation of limit cycles from a centre in R-4 in resonance 1:N
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Data
2009-01-01
Autores
Buzzi, Claudio A.
Llibre, Jaume
Medrado, Joao C.
Torregrosa, Joan
Título da Revista
ISSN da Revista
Título de Volume
Editor
Taylor & Francis Ltd
Resumo
For every positive integer N >= 2 we consider the linear differential centre (x) over dot = Ax in R-4 with eigenvalues +/- i and +/- Ni. We perturb this linear centre inside the class of all polynomial differential systems of the form linear plus a homogeneous nonlinearity of degree N, i.e. (x) over dot Ax + epsilon F(x) where every component of F(x) is a linear polynomial plus a homogeneous polynomial of degree N. Then if the displacement function of order epsilon of the perturbed system is not identically zero, we study the maximal number of limit cycles that can bifurcate from the periodic orbits of the linear differential centre.
Descrição
Palavras-chave
periodic orbits, limit cycles, polynomial vector fields, perturbation, resonance 1:N
Como citar
Dynamical Systems-an International Journal. Abingdon: Taylor & Francis Ltd, v. 24, n. 1, p. 123-137, 2009.