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Zap. Nauchn. Sem. POMI, 2004, Volume 317, Pages 200–212 (Mi znsl721)  

This article is cited in 2 scientific papers (total in 2 papers)

On isomorphism of integrable cases of the Euler equations on the bi-hamiltonian manifolds $e(3)$ and $so(4)$

A. V. Tsiganov

Saint-Petersburg State University

Abstract: The Poisson maps between the Clebsch model and the Schottky system, two Steklov systems, the Kowalevski top and the Neumann system are considered. We prove that these non-canonical transformations of variables are the twisted Poisson maps, which completely define the corresponding pairs of integrable systems.

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English version:
Journal of Mathematical Sciences (New York), 2006, 136:1, 3641–3647

Bibliographic databases:

UDC: 517.9
Received: 26.10.2004

Citation: A. V. Tsiganov, “On isomorphism of integrable cases of the Euler equations on the bi-hamiltonian manifolds $e(3)$ and $so(4)$”, Questions of quantum field theory and statistical physics. Part 18, Zap. Nauchn. Sem. POMI, 317, POMI, St. Petersburg, 2004, 200–212; J. Math. Sci. (N. Y.), 136:1 (2006), 3641–3647

Citation in format AMSBIB
\Bibitem{Tsi04}
\by A.~V.~Tsiganov
\paper On isomorphism of integrable cases of the Euler equations on the bi-hamiltonian manifolds $e(3)$ and $so(4)$
\inbook Questions of quantum field theory and statistical physics. Part~18
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 317
\pages 200--212
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl721}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2120833}
\zmath{https://zbmath.org/?q=an:1136.37347}
\elib{http://elibrary.ru/item.asp?id=9129827}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 136
\issue 1
\pages 3641--3647
\crossref{https://doi.org/10.1007/s10958-006-0188-5}


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    This publication is cited in the following articles:
    1. A. V. Tsiganov, “Compatible Lie–Poisson brackets on the Lie algebras $e(3)$ and $so(4)$”, Theoret. and Math. Phys., 151:1 (2007), 459–473  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Andrey V. Tsiganov, “New variables of separation for the Steklov–Lyapunov system”, SIGMA, 8 (2012), 012, 14 pp.  mathnet  crossref  mathscinet
  • Записки научных семинаров ПОМИ
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