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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Kowalevski top as a reduction of a Hamiltonian system on $\mathfrak {sp}(4, \mathbb {R})^*$
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by C. Ivanescu and A. Savu PDF
Proc. Amer. Math. Soc. 131 (2003), 607-618 Request permission

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
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 607-618
  • MSC (2000): Primary 70H06; Secondary 37J35, 37J15, 70E17
  • DOI: https://doi.org/10.1090/S0002-9939-02-06541-3
  • MathSciNet review: 1933353