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.
@article{urn:eudml:doc:41290,
title = {The null divergence factor.},
journal = {Publicacions Matem\`atiques},
volume = {41},
year = {1997},
pages = {41-56},
mrnumber = {MR1461642},
zbl = {0880.34029},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41290}
}
Chavarriga, Javier; Giacomini, Héctor; Giné, Jaume. The null divergence factor.. Publicacions Matemàtiques, Tome 41 (1997) pp. 41-56. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41290/