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Nelin. Dinam., 2013, Volume 9, Number 2, Pages 229–245 (Mi nd387)  

This article is cited in 3 scientific papers (total in 3 papers)

The Euler–Jacobi–Lie integrability theorem

Valery V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: This paper addresses a class of problems associated with the conditions for exact integrability of a system of ordinary differential equations expressed in terms of the properties of tensor invariants. The general theorem of integrability of the system of $n$ differential equations is proved, which admits $n-2$ independent symmetry fields and an invariant volume $n$-form (integral invariant). General results are applied to the study of steady motions of a continuous medium with infinite conductivity.

Keywords: symmetry field, integral invariant, nilpotent group, magnetic hydrodynamics.

Full text: PDF file (378 kB)
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Document Type: Article
UDC: 517.9
MSC: 34C14
Received: 05.07.2012
Revised: 30.08.2012

Citation: Valery V. Kozlov, “The Euler–Jacobi–Lie integrability theorem”, Nelin. Dinam., 9:2 (2013), 229–245

Citation in format AMSBIB
\Bibitem{Koz13}
\by Valery~V.~Kozlov
\paper The Euler--Jacobi--Lie integrability theorem
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 2
\pages 229--245
\mathnet{http://mi.mathnet.ru/nd387}


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    This publication is cited in the following articles:
    1. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika negolonomnykh sistem, sostoyaschikh iz sfericheskoi obolochki s podvizhnym tverdym telom vnutri”, Nelineinaya dinam., 9:3 (2013), 547–566  mathnet
    2. A. V. Tsyganov, “O share Chaplygina v absolyutnom prostranstve”, Nelineinaya dinam., 9:4 (2013), 711–719  mathnet
    3. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Dinamika trekh vikhreistochnikov”, Nelineinaya dinam., 10:3 (2014), 319–327  mathnet
  • Нелинейная динамика
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