  We derive necessary conditions for integrability in the Liouville sense of
natural Hamiltonian systems with homogeneous potential of degree zero. We
derive these conditions through an analysis of the differential Galois group of
variational equations along a particular solution generated by a non-zero
solution $\vd\in\C^n$ of nonlinear equations $\grad V(\vd)=\vd$. We proved that
if the system integrable then the Hessian matrix $V''(\vd)$ has only integer
eigenvalues and is semi-simple.
