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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Kowalevski top as a reduction of a Hamiltonian system on $\mathfrak{sp}(4, \mathbb{R} )^*$


Authors: C. Ivanescu and A. Savu
Journal: Proc. Amer. Math. Soc. 131 (2003), 607-618
MSC (2000): Primary 70H06; Secondary 37J35, 37J15, 70E17
Published electronically: May 22, 2002
MathSciNet review: 1933353
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Abstract: We show that the Kowalevski top and Kowalevski gyrostat are obtained as a reduction of a Hamiltonian system on $\mathfrak{sp}(4,\mathbb{R} )^*$. Therefore the Lax-pair representations for the Kowalevski top and Kowalevski gyrostat are obtained via a direct method by transforming the canonical Lax-pair representation of a system on $\mathfrak{sp}(4, \mathbb{R} )^*$. Also we show that the nontrivial integral of motion of the Kowalevski top comes from a Casimir function of the Lie-Poisson algebra $\mathfrak{sp}(4, \mathbb{R} )^*$.


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Additional Information

C. Ivanescu
Affiliation: Fields Institute, 222 College Street, Toronto, Ontario, Canada M5T 3J1
Email: civanesc@fields.utoronto.ca

A. Savu
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email: ana@math.toronto.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06541-3
PII: S 0002-9939(02)06541-3
Keywords: Heavy top, Kowalevski top, Lax-pair representation
Received by editor(s): March 1, 2001
Received by editor(s) in revised form: September 6, 2001
Published electronically: May 22, 2002
Additional Notes: This research was supported by a J.R. Gilkinson Smith and University of Toronto fellowship
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2002 American Mathematical Society