山中祥五 氏
2018年11月8日(木) 13時00分
総合研究10号館317号室(セミナー室)
Birkhoff normal forms are special normal forms of Hamiltonian systems near equilibria and the problem of determining whether they are non-integrable has attracted much attention in the field of dynamical systems. In this talk we prove that three-degree-of-freedom Birkhoff normal forms are non-integrable when they are in 1:2:ω resonance for ω =1,2 or 4. Recently, Christov [1] also studied non-integrability of the same normal forms although his proofs contained some errors.[1] O. Christov, Non-integrability of first order resonances in Hamiltonian systems in three degrees of freedom, Celest. Mech. Dyn. Astr., 112 (2012), 149-167.