The null divergence factor (Q1365654)

The paper shows how to construct systems with a finite number of limit cycles and systems of center type on the plane. A tool of construction is the so-called null divergence factor which is a function allowing to define an integrating factor of system and to guarantee the existence of an integral. The proposed method is a generalization of the classical Darboux method of construction integrable systems. The proposed construction is applied to the investigation of polynomial systems.