On the number of limit cycles bifurcating from a non-global degenerated center |
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Authors: | Armengol Gasull Chengzhi Li Changjian Liu |
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Institution: | a Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain b LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China |
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Abstract: | We give an upper bound for the number of zeros of an Abelian integral. This integral controls the number of limit cycles that bifurcate, by a polynomial perturbation of arbitrary degree n, from the periodic orbits of the integrable system , where H is the quasi-homogeneous Hamiltonian H(x,y)=x2k/(2k)+y2/2. The tools used in our proofs are the Argument Principle applied to a suitable complex extension of the Abelian integral and some techniques in real analysis. |
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Keywords: | Abelian integral Limit cycle Planar vector field Degenerated center |
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