Phase portraits of reversible linear differential systems with cubic homogeneous polynomial nonlinearities having a non-degenerate center at the origin

Abstract

In this paper we classify the global phase portraits of all reversible linear differential systems with cubic homogeneous polynomial nonlinearities defined in the plane and having a non degenerate center at the origin. The reversibility is given by a linear involution having a fixed set of dimension 1. © 2008 Birkhäuser Verlag Basel/Switzerland.