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

DOI10.1016/S0375-9601(00)00445-XzbMath1115.37336arXivnlin/0006045MaRDI QIDQ997673

Leonid Faybusovich, Michael I. Gekhtman

Publication date: 7 August 2007

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0006045

zbMATH Keywords

integrable latticescompatible Poisson structures

Mathematics Subject Classification ID

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

Related Items (13)

MULTIPLE HAMILTONIAN STRUCTURE OF BOGOYAVLENSKY–TODA LATTICES ⋮ Two-weight Hilbert transform and Lipschitz property of Jacobi matrices associated to hyperbolic polynomials ⋮ Towards a cluster structure on trigonometric zastava ⋮ Action-angle map and duality for the open Toda lattice in the perspective of Hamiltonian reduction ⋮ Poisson geometry of directed networks in an annulus ⋮ An integrable system on the moduli space of rational functions and its variants. ⋮ Generalized Bäcklund-Darboux transformations for Coxeter-Toda flows from a cluster algebra perspective ⋮ A non-local Poisson bracket for Coxeter--Toda lattices ⋮ Darboux-Nijenhuis variables for open generalized Toda chains ⋮ The hierarchy of Poisson brackets for the open Toda lattice and its spectral curves ⋮ Integrable hierarchies and the modular class ⋮ Poisson brackets of orthogonal polynomials ⋮ Multi‐Hamiltonian structure for the finite defocusing Ablowitz‐Ladik equation

Cites Work

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