Special Session 59: Central configurations, periodic solutions, variational method and beyond in celestial mechanics
Contents
It is a big problem to distinguish between integrable and non-integrable Hamiltonian systems.
I will provide a new approach to prove the non-integrability of homogeneous Hamiltonian systems with two degrees of freedom. The homogeneous degree can be taken from real values (not necessarily integer). The proof is based on the blowing-up theory which McGehee established in the collinear three-body problem. I will also compare our result with Molares-Ramis theory which is the strongest theory in this field.