The integrability of two symplectic maps that can be considered as discrete-time analogs of the Gamier and Neumann systems is established in the framework of the r-matrix approach, starting from their Lax representation. In contrast with the continuous case, the r-matrix for such discrete systems turns out to be of dynamical type; remarkably, the induced Poisson structure appears as a linear combination of compatible ''more elementary'' Poisson structures. It is also shown that the Lax matrix naturally leads to define separation variables, whose discrete and continuous dynamics are investigated.

RAGNISCO O (1995). DYNAMICAL R-MATRICES FOR INTEGRABLE MAPS. PHYSICS LETTERS A, 198(4), 295-305 [10.1016/0375-9601(95)00056-9].

DYNAMICAL R-MATRICES FOR INTEGRABLE MAPS

RAGNISCO, Orlando
1995

Abstract

The integrability of two symplectic maps that can be considered as discrete-time analogs of the Gamier and Neumann systems is established in the framework of the r-matrix approach, starting from their Lax representation. In contrast with the continuous case, the r-matrix for such discrete systems turns out to be of dynamical type; remarkably, the induced Poisson structure appears as a linear combination of compatible ''more elementary'' Poisson structures. It is also shown that the Lax matrix naturally leads to define separation variables, whose discrete and continuous dynamics are investigated.
RAGNISCO O (1995). DYNAMICAL R-MATRICES FOR INTEGRABLE MAPS. PHYSICS LETTERS A, 198(4), 295-305 [10.1016/0375-9601(95)00056-9].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/138018
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