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Fundamentalnaya i Prikladnaya Matematika, 2010, Volume 16, Issue 4, Pages 3–229 (Mi fpm1332)  

This article is cited in 80 scientific papers (total in 80 papers)

Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems

V. V. Trofimov, M. V. Shamolin

M. V. Lomonosov Moscow State University
References:
Abstract: This paper presents results referred to geometric invariant theory of completely integrable Hamiltonian systems and also to the classification of integrable cases of low-dimensional and high-dimensional rigid body dynamics in a nonconservative force field. The latter problems are described by dynamical systems with variable dissipation. The first part of the work is the base the doctorial dissertation of V. V. Trofimov (1953–2003), which was in parts already published. However, in the present entire form, it was not appeared, and we decided to fill in this gap. The second part is a development of the results presented in the doctorial dissertation of M. V. Shamolin, and it was not appeared in the present variant. These two parts well complement one another, which initiated this work (its sketches already appeared in 1997).
English version:
Journal of Mathematical Sciences (New York), 2012, Volume 180, Issue 4, Pages 365–530
DOI: https://doi.org/10.1007/s10958-012-0650-5
Bibliographic databases:
Document Type: Article
UDC: 517+531.01
Language: Russian
Citation: V. V. Trofimov, M. V. Shamolin, “Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems”, Fundam. Prikl. Mat., 16:4 (2010), 3–229; J. Math. Sci., 180:4 (2012), 365–530
Citation in format AMSBIB
\Bibitem{TroSha10}
\by V.~V.~Trofimov, M.~V.~Shamolin
\paper Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems
\jour Fundam. Prikl. Mat.
\yr 2010
\vol 16
\issue 4
\pages 3--229
\mathnet{http://mi.mathnet.ru/fpm1332}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2786542}
\transl
\jour J. Math. Sci.
\yr 2012
\vol 180
\issue 4
\pages 365--530
\crossref{https://doi.org/10.1007/s10958-012-0650-5}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84855824732}
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  • https://www.mathnet.ru/eng/fpm/v16/i4/p3
  • This publication is cited in the following 80 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Фундаментальная и прикладная математика
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    Abstract page:1068
    Full-text PDF :482
    References:94
    First page:2
     
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