Bifurcation of limit cycles from a centre in R-4 in resonance 1:N

Buzzi, Claudio A.; Llibre, Jaume; Medrado, Joao C.; Torregrosa, Joan

Bifurcation of limit cycles from a centre in R-4 in resonance 1:N

Data

2009-01-01

Autores

Editor

Taylor & Francis Ltd

Tipo

Artigo

Direito de acesso

Acesso restrito

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.