Application of Morales-Ramis method to the class of Hamiltonian systems with homogeneous potentials.

In this second part we show the Morales-Ramis theory in action. Namely, the class of Hamiltonian systems with two degrees of freedom and homogeneous potential of degree $k>2$ is analysed. As results the rigorous proofs of the non-integrability and integrable potentials are obtained. Also some open problems will be presented.