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
1995-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
