Inverse Jacobian multipliers and Hopf bifurcation on center manifolds

Abstract

In this paper we consider a class of higher dimensional differential systems in ${\mathbb{R}}^n$ 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 $C^{\infty }$ 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.

22. Journal of Differential Equation, 2014

References in corpus (2)

• Analytic integrable systems: Analytic normalization and embedding flows
• The embedding flows of $C^{\infty }$ hyperbolic diffeomorphisms