Sisteme diferenţiale cubice cu un fascicul de drepte afine invariante şi linia de la infinit de multiplicitatea doi [Articol]

Abstract

In this paper we show that in the class of cubic differential systems with a bundle of three affine invariant straight lines and the line at infinity of multiplicity two each critical point with pure imaginary eigenvalues is of the center type if and only if the first Lyapunov quantity vanish. In all the cases of center the systems are Darboux integrable.