Dynamics aspects in a galactic type Hamiltonian

We are interested in the investigation of the dynamics of the canonical system of differential equations deriving from the galactic type Hamiltonian given by the quartic function H=12(y12+ω12x12)+δ2(y22+ω22x22)−ϵx12x22 from an analytical point of view according to the real parameters δδ and ϵϵ. Similar Hamiltonians have been considered by several investigators in order to study the motion in the central parts of elliptical galaxies.