Nondegenerate and Nilpotent Centers for a Cubic System of Differential Equations

  1. Algaba, Antonio 1
  2. García, Cristóbal 1
  3. Giné, Jaume 2
  1. 1 Universidad de Huelva
    info

    Universidad de Huelva

    Huelva, España

    ROR https://ror.org/03a1kt624

  2. 2 Universitat de Lleida
    info

    Universitat de Lleida

    Lleida, España

    ROR https://ror.org/050c3cw24

Revista:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Año de publicación: 2019

Volumen: 18

Número: 1

Páginas: 333-345

Tipo: Artículo

DOI: 10.1007/S12346-018-0301-4 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Qualitative theory of dynamical systems

Resumen

We consider the autonomous system of differential equations of the form x˙=P1(x,y)+P2(x,y),y˙=Q1(x,y)+Q3(x,y),where Pi and Qi are homogeneous polynomials of degree i. For such systems we provide the necessary and sufficient conditions to have a center at the origin. In fact this family only has nondegenerate and nilpotent centers.

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