Inverse Jacobian multipliers and Hopf bifurcation on center manifolds |
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Authors: | Xiang Zhang |
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Institution: | Department of Mathematics, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, People''s Republic of China |
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Abstract: | In this paper we consider a class of higher dimensional differential systems in Rn 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∞ 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. |
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Keywords: | 34A34 37C10 34C14 37G05 |
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