Generically, Arnold-Liouville systems cannot be bi-Hamiltonian

DOI10.3842/SIGMA.2021.096zbMath1484.37063arXiv2105.11123OpenAlexW3210426406MaRDI QIDQ2666001

Robert Brouzet, Hassan Boualem

Publication date: 22 November 2021

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.11123

zbMATH Keywords

action-angle coordinatesbi-Hamiltonian systemcompletely integrable Hamiltonian systemArnold-Liouville theoremFréchet topologychange of coordinatesseparability of functions

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) 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 topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

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