  It is a big problem to distinguish between integrable and non-integrable
Hamiltonian systems. We provide a new approach to prove the non-integrability
of homogeneous Hamiltonian systems with two degrees of freedom.
  The homogeneous degree can be chosen from real values (not necessarily
integer). The proof is based on the blowing-up theory which McGehee established
in the collinear three-body problem. We also compare our result with
Molares-Ramis theory which is the strongest theory in this field.
