Inverse Jacobian multipliers and Hopf bifurcation on center manifolds.

Abstract: In this paper we consider a class of higher dimensional differential systems in which have a two dimensional center manifold at the origin with a pair of pure imaginary eigenvalues. First we characterize the existence of either analytic or inverse Jacobian multipliers of the systems around the origin, which is either a center or a focus on the center manifold. Later we study the cyclicity of the system at the origin through Hopf bifurcation by using the vanishing multiplicity of the inverse Jacobian multiplier. [Copyright &y& Elsevier]