ℤ2-symmetric planar polynomial Hamiltonian systems of degree 3 with nilpotent centers

Abstract

We provide the normal forms of all ℤ2-symmetric planar polynomial Hamiltonian systems of degree 3 having a nilpotent center at the origin. Furthermore, we complete the classification of the global phase portraits in the Poincare disk of the above systems initiated by Dias, Llibre and Valls [9].