
SIGMA 2 (2006), 098, 10 pages mathph/0610083
https://doi.org/10.3842/SIGMA.2006.098
Contribution to the Vadim Kuznetsov Memorial Issue
Invariant Varieties of Periodic Points for the Discrete Euler Top
Satoru Saito ^{a} and Noriko Saitoh ^{b}
^{a)} Hakusan 41910, Midoriku, Yokohama 2260006, Japan
^{b)} Applied Mathematics, Yokohama National University,
Hodogayaku, Yokohama 2408501, Japan
Received October 28, 2006, in final form
December 16, 2006; Published online December 30, 2006
Abstract
The behaviour of periodic points of discrete Euler top is studied.
We derive invariant varieties of periodic points explicitly.
When the top is axially symmetric they are specified by some particular
values of the angular velocity along the axis of symmetry, different for each period.
Key words:
invariant varieties of periodic points; discrete Euler top; integrable map.
pdf (190 kb)
ps (149 kb)
tex (13 kb)
references
 Kuznetsov V.B., Nijhoff F.W. (Editors), Kowalevski workshop on mathematical methods of regular dynamics,
J. Phys. A: Math. Gen., 2001, V.34.
 Kuznetsov V.B., Kowalevski top revisited,
nlin.SI/0110012.
 Saito S., Saitoh N., Invariant varieties of periodic points for some higher dimensional
integrable maps, J. Phys. Soc. Japan, 2007, V.76, to appear,
mathph/0610069.
 Bobenko A.I., Lorbeer B., Suris Yu.B., Integrable discretization of the Euler map,
J. Math. Phys. A: Math. Gen., 1988, V.39, 66686683.
 Hirota R., Kimura K., Discretization of the Euler top, J. Phys. Soc. Japan, 2000, V.69, 627630.
 Hirota R., Takahashi D., Discrete and ultradiscrete systems, Tokyo, Kyoritsu Shuppan,
2003 (in Japanese).
 Fedorov Yu., Integrable flows and Bäcklund transformations on extended Stiefel
varieties with application to the Euler top on the Lie group SO(3), J. Nonlinear Math. Phys.,
2005, V.12, 7794, nlin.SI/0505045.
 Marsden J., West M., Discrete mechanics and variational integrators,
Acta Numerica, 2001, V.10, 357514.

