A non-local Poisson bracket for Coxeter--Toda lattices

DOI10.4064/cm7700-4-2019zbMath1452.37062arXiv1609.08769OpenAlexW3006701622MaRDI QIDQ5126655

Eber Chuño

Publication date: 20 October 2020

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.08769

zbMATH Keywords

compatible Poisson bracketsMoser mapAtiyah-Hitchin bracketCoxeter-Toda latticegeneralized Bäcklund-Darboux transformations

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Poisson manifolds; Poisson groupoids and algebroids (53D17) Applications of Lie algebras and superalgebras to integrable systems (17B80) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37)

Uses Software

• Maple

Cites Work

• Generalized Bäcklund-Darboux transformations for Coxeter-Toda flows from a cluster algebra perspective
• Poisson brackets on rational functions and multi-Hamiltonian structure for integrable lattices
• Integrability of characteristic Hamiltonian systems on simple Lie groups with standard Poisson Lie structure
• Factorization dynamics and Coxeter-Toda lattices
• Poisson geometry of directed networks in a disk
• Relativistic Toda systems
• Elementary Toda orbits and integrable lattices
• Inverse moment problem for elementary co-adjoint orbits
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• Double Bruhat cells and total positivity
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