Linear type global centers of cubic Hamiltonian systems symmetric with respect to the x-axis

Abstract

A polynomial differential system of degree 2 has no global centers (that is, centers defined in all the plane except the fixed point). In this paper we characterize the global centers of cubic Hamiltonian systems symmetric with respect to the x-axis, and such that the center has purely imaginary eigenvalues.

Keywords

• center
• global center
• hamiltonian system
• symmetry with respect to the x-axis
• cubic polynomial differential system