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Mathematics of the USSR-Izvestiya, 1992, Volume 38, Issue 1, Pages 69–90
DOI: https://doi.org/10.1070/IM1992v038n01ABEH002187 (Mi im1026) 		 
This article is cited in 52 scientific papers (total in 52 papers)

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

A. V. Bolsinov
English version PDF (1493 kB) Citations (52)
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DOI: https://doi.org/10.1070/IM1992v038n01ABEH002187
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.
Received: 13.07.1989
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1991, Volume 55, Issue 1, Pages 68–92
Bibliographic databases:
UDC: 513.944
MSC: 58F07
Language: English
Original paper language: Russian
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
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\paper Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution
\jour Izv. Akad. Nauk SSSR Ser. Mat.
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\issue 1
\pages 68--92
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\transl
\jour Math. USSR-Izv.
\yr 1992
\vol 38
\issue 1
\pages 69--90
\crossref{https://doi.org/10.1070/IM1992v038n01ABEH002187}
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  • https://doi.org/10.1070/IM1992v038n01ABEH002187
  • https://www.mathnet.ru/eng/im/v55/i1/p68
    • This publication is cited in the following 52 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:976
    Russian version PDF:388
    English version PDF:25
    References:90
    First page:3
     
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