The null divergence factor

• Autores: Hector J. Giacomini , Jaume Giné Mesa , Javier Chavarriga Soriano
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 41, Nº 1, 1997 (Ejemplar dedicado a: Proceedings of the Symposium on Planar Vector Fields), págs. 41-56
• Idioma: inglés
• DOI: 10.5565/publmat_41197_03
• Títulos paralelos:
  • Factor de divergencia nulo
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• Resumen

  • Let $(P, Q)$ be a $C^{1}$ vector field defined in a open subset $U \subset R^{2}$. We call a null divergence factor a $C^{1}$ solution $V(x, y)$ of the equation $P \frac{\partial V}{\partial x} + Q \frac{\partial V}{\partial y} = \left(\frac{\partial P}{\partial x} + \frac{\partial Q}{\partial y}\right) \, V$. In previous works it has been shown that this function plays a fundamental role in the problem of the center and in the determination of the limit cycles. In this paper we show how to construct systems with a given null divergence factor. The method presented in this paper is a generalization of the classical Darboux method to generate integrable systems.