Dynamics of locally linearizable complex two dimensional cubic Hamiltonian systems

Abstract

The aim of this paper is to characterize global dynamics of locally linearizable complex two dimensional cubic Hamiltonian systems. By finding invariants, we prove that their associated real phase space R 4 is foliated by two dimensional invariant surfaces, which could be either simple connected, or double connected, or triple connected, or quadruple connected. On each of the invariant surfaces all regular orbits are heteroclinic ones, which connect two singularities, either both finite, or one finite and another at infinity, or both at infinity, and all these situations are realizable.