Regular and Chaotic Dynamics

, Volume 18, Issue 4, pp 329–343 | Cite as

The Euler-Jacobi-Lie integrability theorem

Article

Abstract

This paper addresses a class of problems associated with the conditions for exact integrability of systems 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 continuum with infinite conductivity.

Keywords

symmetry field integral invariant nilpotent group magnetic hydrodynamics 

MSC2010 numbers

34C14 

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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.V. A. Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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