# Inverse Jacobian multipliers and Hopf bifurcation on center manifolds

Date:
20.01.14
Times:
15:30 to 16:30
Place:
CRM - Auditori (C1/034)
Speaker:
Xiang Zhang
University:
Shanghai Jiaotong University

#### Abstract:

In this talk I will report on a new result on analytic differential systems in $\mathbb{R}^n$ with a pair of pure imaginary eigenvalues. We first characterize the existence of either analytic or $\mathcal{C}^\infty$ inverse Jacobian multipliers of the systems around the origin, which is either a center or a focus on the center manifold. Then we study the cyclicity of the system at the origin through Hopf bifurcation via the vanishing multiplicity of the inverse Jacobian multiplier.