Nondegenerate linearizable centres of complex planar quadratic and symmetric cubic systems in C2

• Autores: C. Rousseau, Colin Christopher
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 45, Nº 1, 2001, págs. 95-123
• Idioma: inglés
• DOI: 10.5565/publmat_45101_04
• Títulos paralelos:
  • Centros linealizables no degenerados de sistemas cúbicos simétricos y cuadráticos planos complejos en C2
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• Resumen

  • 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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