Hidden structure of the Lie algebra of symmetries

C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (1), 2005 pp. 14–19
(Received: 2004-02-25 )

O.I. Bogoyavlenskij, Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6; email: bogoyavl@mast.queensu.ca

Abstract/Résumé:

For any dynamical system, a hidden structure of its Lie algebra of symmetries is disclosed. The structure is based on a new infinite series of the canonically defined Lie subalgebras and on their commutator relations.

Pour n’importe quel système dynamique, une structure cachée de son algèbre de Lie de symétries est révélée. Cette structure découle d’une nouvelle série de sous-algèbres de Lie canoniquement définies et de leurs relations de commutateurs.

Keywords:

AMS Subject Classification: Completely integrable systems; topological structure of phase space; integration methods 37J35

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