Bifurcation Of Limit Cycles From A Centre In R~4 In Resonance 1:n

摘要

For every positive integer N ≥ 2 we consider the linear differential centre x = 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 = Ax + εF(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 e of the perturbed system is hot identically zero, we study the maximal number of limit cycles that can bifurcate from the periodic orbits of the linear differential centre.