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Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices. (English) Zbl 1115.37336
Summary: We introduce a family of compatible Poisson brackets on the space of rational functions with denominator of a fixed degree and use it to derive a multi-Hamiltonian structure for a family of integrable lattice equations that includes both the standard and the relativistic Toda lattices.

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K60 Lattice dynamics; integrable lattice equations
53D17 Poisson manifolds; Poisson groupoids and algebroids
70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
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