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: uwano@kuamp.kyoto-u.ac.jp, or
vinitsky@thsun1.jinr.dubna.su)