Department of Applied Mathematics & Physics, Kyoto Univiversity

Technical Report #97010 (November, 1997)

'Inverse-GITA' for an Inverse Problem of the Birkhoff-Gustavson Normal Form Method
by N.A.Chekanov, M.Hongo, V.A.Rostovtsev, Y.Uwano and S.I.Vinitsky

When a dynamical system is studied successfully through the BGNF (Birkhoff-Gustavson normal form) method, one may pose an 'inverse problem' as follows: How can one specify explicitly a class of dynamical systems which are reduced to the same BGNF up to a certain order ? To settle this 'inverse problem', the symbolic computing procedure named 'the inverse-GITA' is proposed in this paper, which is realized by inverting GITA, the symbolic computing procedure to calculate BGNF. As an application of the inverse-GITA, it is reported that the inverse-GITA provides a class of integrable Hamiltonian systems of Liouville-type which share the same BGNF Hamiltonian with the regularized system of a planar hydrogen atom with the linear Stark effect. (To appear in Soviet Journal of Nuclear Physics, e-mail:, or