Center cyclicity of a family of quartic polynomial differential system |
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Authors: | Isaac A. García Jaume Llibre Susanna Maza |
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Affiliation: | 1.Departament de Matemàtica,Universitat de Lleida,Lleida,Spain;2.Departament de Matemàtiques,Universitat Autònoma de Barcelona,Bellaterra, Barcelona,Spain |
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Abstract: | In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as $$dot{z} = i z + z bar{z}big(A z^2 + B z bar{z} + C bar{z}^2 big),$$ where ({A,B,C in mathbb{C}}). We give an upper bound for the cyclicity of any nonlinear center at the origin when we perturb it inside this family. Moreover we prove that this upper bound is sharp. |
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