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Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices

L. Faybusovich·M. Gekhtman
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Abstract

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.

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L. Faybusovich, M. Gekhtman. 2000-06-26. Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices. https://arxiv.org/abs/nlin/0006045

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