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Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 1, Pages 68–92 (Mi izv1026)  

This article is cited in 35 scientific papers (total in 35 papers)

Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution

A. V. Bolsinov

Abstract: This paper presents a method for checking completeness of families of functions which are in involution with respect to compatible Poisson brackets. Several examples of compatible Poisson brackets on duals of Lie algebras are considered, as well as the associated involutive function families and Hamiltonian systems. The transitions of Liouville tori for some nonintegrable Hamiltonian systems, notably the equations of motion for a higher dimensional rigid body, are described.

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English version:
Mathematics of the USSR-Izvestiya, 1992, 38:1, 69–90

Bibliographic databases:

UDC: 513.944
MSC: 58F07
Received: 13.07.1989

Citation: A. V. Bolsinov, “Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution”, Izv. Akad. Nauk SSSR Ser. Mat., 55:1 (1991), 68–92; Math. USSR-Izv., 38:1 (1992), 69–90

Citation in format AMSBIB
\by A.~V.~Bolsinov
\paper Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1991
\vol 55
\issue 1
\pages 68--92
\jour Math. USSR-Izv.
\yr 1992
\vol 38
\issue 1
\pages 69--90

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    2. I. Z. Golubchik, V. V. Sokolov, “Compatible Lie Brackets and Integrable Equations of the Principal Chiral Model Type”, Funct. Anal. Appl., 36:3 (2002), 172–181  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    4. A. V. Tsiganov, “On isomorphism of integrable cases of the Euler equations on the bi-hamiltonian manifolds $e(3)$ and $so(4)$”, J. Math. Sci. (N. Y.), 136:1 (2006), 3641–3647  mathnet  crossref  mathscinet  zmath  elib
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    17. Vorontsov A.S., “Kronekerovy indeksy algebry li i otsenka stepenei invariantov”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2011, no. 1, 26–30  elib
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    30. M. A. Tuzhilin, “Bihamilon structure and singularities of momentum mapping for Lagrange top”, Moscow University Mathematics Bulletin, 70:2 (2015), 74–78  mathnet  crossref  mathscinet
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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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