Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in $\mathbb{C}^2$ | Zendy

Colin Christopher | Zendy; Christiane Rousseau | Zendy

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Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in $\mathbb{C}^2$

Author(s) -

Colin Christopher,

Christiane Rousseau

Publication year - 2001

Publication title -

publicacions matemàtiques

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.99

H-Index - 27

eISSN - 2014-4350

pISSN - 0214-1493

DOI - 10.5565/publmat_45101_04

Subject(s) - mathematics , quadratic equation , generalization , planar , pure mathematics , complex plane , class (philosophy) , plane (geometry) , type (biology) , mathematical analysis , geometry , computer science , computer graphics (images) , ecology , artificial intelligence , biology

In this paper we consider complex differential systems in the plane, which are linearizable in the neighborhood of a nondegenerate centre. We find necessary and sufficient conditions for linearizability for the class of complex quadratic systems and for the class of complex cubic systems symmetric with respect to a centre. The sufficiency of these conditions is shown by exhibiting explicitly a linearizing change of coordinates, either of Darboux type or a generalization of it

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