Three-degree-of-freedom Hamiltonian systems with 1:2:ω (ω = 1,2,3,4) resonances have been studied. We consider the case that they are in Birkhoff normal form. It is known that Birkhoff normal forms with 1:2:2 resonance are integrable. However, Birkhoff normal forms with 1:2:ω (ω = 1,3,4) resonances are thought to be nonintegrable without the known integrable cases. Following , we prove their nonintegrability for some parameters.
 O. Christov, Non-integrability of first order resonances in Hamiltonian systems in three degrees of freedom, Celest. Mech. Dyn. Astr. 112 (2012), 149--167.