Global centers of a class of cubic polynomial differential systems

Abstract

A difficult classical problem in the qualitative theory of differential systems in the plane R2 is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center p such that R2\{p} is filled with periodic orbits. In this paper we classify the global centers of the family of real polynomial differential systems of degree 3 that in complex notation write (Formula presented.) where w=x+iy and Ak∈C for k=3,4,5,6.