On a class of global centers of linear systems with quintic homogeneous nonlinearities

Abstract

One of the classical and difficult problems in the qualitative theory of differential systems in the plane is the characterization of their centers. In this paper we characterize the linear and nilpotent global centers of polynomial differential systems with quintic homogeneous terms, with the symmetry (x,y,t) → (−x,y,−t) and without infinite singular points.