Generalized tops and moment maps to loop algebras

DOI10.1063/1.529241zbMath0733.70012OpenAlexW2005574024MaRDI QIDQ3359812

J. Harnad, Jacques Hurtubise

Publication date: 1991

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529241

zbMATH Keywords

symmetry groupsintegrable Hamiltonian systemsHamiltonian reductionLax equationsloop algebrasgeneralized tops

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Loop groups and related constructions, group-theoretic treatment (22E67) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

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Integrable systems and algebraic surfaces ⋮ Multi-Hamiltonian structures for r-matrix systems

Cites Work

• A new integrable case of the motion of the 4-dimensional rigid body
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• The Kowalewski top 99 years later: a Lax pair, generalizations and explicit solutions
• Isospectral Hamiltonian flows in finite and infinite dimensions. II: Integration of flows
• Dual moment maps into loop algebras