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New symplectic maps: integrability and Lax representation. (English) Zbl 0890.58018

Summary: A new family of integrable symplectic maps is reduced from the Toda hierarchy via constraint for a higher flow of the hierarchy in terms of square eigenfunctions. Their integrability and Lax representation are deduced systematically from the discrete zero-curvature representation of the Toda hierarchy. Also a discrete zero-curvature representation for the Toda hierarchy with sources is presented.

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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