The authors consider a tri-Hamiltonian formulation giving rise not to a single chain of recurrences but a two-dimensional scheme labelled by two indices. An application of this new notion is considered in the case of the periodic Toda lattice. A new (linear) Poisson structure is defined on a subspace of the Kupershmidt algebra isomorphic to the space of Hermitian matrices. This new Poisson structure together with the two well-known linear and quadratic Toda brackets gives rise to a tri-Hamiltonian extension of the periodic lattice which fits the two-dimensional scheme mentioned above. Some explicit examples of the construction are given.

A trihamiltonian extension of the Toda lattice

ANDRA', Chiara;DEGIOVANNI, LUCA;MAGNANO, Guido
2007

Abstract

The authors consider a tri-Hamiltonian formulation giving rise not to a single chain of recurrences but a two-dimensional scheme labelled by two indices. An application of this new notion is considered in the case of the periodic Toda lattice. A new (linear) Poisson structure is defined on a subspace of the Kupershmidt algebra isomorphic to the space of Hermitian matrices. This new Poisson structure together with the two well-known linear and quadratic Toda brackets gives rise to a tri-Hamiltonian extension of the periodic lattice which fits the two-dimensional scheme mentioned above. Some explicit examples of the construction are given.
57
863
880
Classical integrable systems; Symplectic geometry; Periodic Toda lattice; Trihamiltonian systems; Classical r-matrix
C. ANDRA'; L. DEGIOVANNI; G. MAGNANO
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/7114
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