SIGMA 2 (2006), 098, 10 pages      math-ph/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 4-19-10, Midori-ku, Yokohama 226-0006, Japan
^b) Applied Mathematics, Yokohama National University, Hodogaya-ku, Yokohama 240-8501, 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.

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references

1. Kuznetsov V.B., Nijhoff F.W. (Editors), Kowalevski workshop on mathematical methods of regular dynamics, J. Phys. A: Math. Gen., 2001, V.34.
2. Kuznetsov V.B., Kowalevski top revisited, nlin.SI/0110012.
3. Saito S., Saitoh N., Invariant varieties of periodic points for some higher dimensional integrable maps, J. Phys. Soc. Japan, 2007, V.76, to appear, math-ph/0610069.
4. Bobenko A.I., Lorbeer B., Suris Yu.B., Integrable discretization of the Euler map, J. Math. Phys. A: Math. Gen., 1988, V.39, 6668-6683.
5. Hirota R., Kimura K., Discretization of the Euler top, J. Phys. Soc. Japan, 2000, V.69, 627-630.
6. Hirota R., Takahashi D., Discrete and ultradiscrete systems, Tokyo, Kyoritsu Shuppan, 2003 (in Japanese).
7. 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, 77-94, nlin.SI/0505045.
8. Marsden J., West M., Discrete mechanics and variational integrators, Acta Numerica, 2001, V.10, 357-514.