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On the Lie algebra structures connected with Hamiltonian dynamical systems

On the Lie algebra structures connected with Hamiltonian dynamical systems

We construct the hierarchies of master symmetries constituting Virasoro-type algebras for the Hamiltonian vector fields preserving a recursion operator. Similarly, repeatedly contracting a Hamiltonian vector field with the corresponding recursion operator, we define an Abelian Lie algebra of the thu...

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Bibliographic Details
Main Author: Smirnov, R.G.
Format: Article
Language:English
Published: Інститут математики НАН України 1997
Series:Український математичний журнал
Subjects:
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Online Access:http://dspace.nbuv.gov.ua/handle/123456789/157068
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Summary:We construct the hierarchies of master symmetries constituting Virasoro-type algebras for the Hamiltonian vector fields preserving a recursion operator. Similarly, repeatedly contracting a Hamiltonian vector field with the corresponding recursion operator, we define an Abelian Lie algebra of the thus obtained hierarchy of vector fields. The approach is shown to be applicable for the Volterra and Toda lattices.

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