On the integrability of a three-dimensional cored galactic Hamiltonian

We characterize when the three-dimensional cored galactic Hamiltonian system with Hamiltonian H=12(px2+py2+pz2q)+1+x2+y2+z2q, is completely meromorphically integrable when q∈[0.36,1]q∈[0.36,1]. The key point for this characterization is to transform the non-polynomial cored Hamiltonian system into a polynomial one.