# The null divergence factor.

• Volume: 41, Issue: 1, page 41-56
• ISSN: 0214-1493

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## Abstract

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Let (P,Q) be a C1 vector field defined in a open subset U ⊂ R2. We call a null divergence factor a C1 solution V (x, y) of the equation P ∂V/∂x + Q ∂V/ ∂y = ( ∂P/∂x + ∂Q/∂y ) 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.

## How to cite

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Chavarriga, Javier, Giacomini, Héctor, and Giné, Jaume. "The null divergence factor.." Publicacions Matemàtiques 41.1 (1997): 41-56. <http://eudml.org/doc/41290>.

@article{Chavarriga1997,
abstract = {Let (P,Q) be a C1 vector field defined in a open subset U ⊂ R2. We call a null divergence factor a C1 solution V (x, y) of the equation P ∂V/∂x + Q ∂V/ ∂y = ( ∂P/∂x + ∂Q/∂y ) 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.},
author = {Chavarriga, Javier, Giacomini, Héctor, Giné, Jaume},
journal = {Publicacions Matemàtiques},
keywords = {Formas cuadráticas; Campos vectoriales; Sistemas diferenciales; Ecuaciones en derivadas parciales no lineales; Ecuaciones polinómicas; Propiedad de Darboux; integrating factor; Darboux method; limit cycle; center type; polynomial systems},
language = {eng},
number = {1},
pages = {41-56},
title = {The null divergence factor.},
url = {http://eudml.org/doc/41290},
volume = {41},
year = {1997},
}

TY - JOUR
AU - Chavarriga, Javier
AU - Giacomini, Héctor
AU - Giné, Jaume
TI - The null divergence factor.
JO - Publicacions Matemàtiques
PY - 1997
VL - 41
IS - 1
SP - 41
EP - 56
AB - Let (P,Q) be a C1 vector field defined in a open subset U ⊂ R2. We call a null divergence factor a C1 solution V (x, y) of the equation P ∂V/∂x + Q ∂V/ ∂y = ( ∂P/∂x + ∂Q/∂y ) 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.
LA - eng
KW - Formas cuadráticas; Campos vectoriales; Sistemas diferenciales; Ecuaciones en derivadas parciales no lineales; Ecuaciones polinómicas; Propiedad de Darboux; integrating factor; Darboux method; limit cycle; center type; polynomial systems
UR - http://eudml.org/doc/41290
ER -

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