Degenerately Integrable Systems

The subject of this paper is degenerate integrability in Hamiltonian mechanics. We start with a short survey of degenerate integrability. The first section contains basic notions. It is followed by a number of examples which include the Kepler system, Casimir models, spin Calogero models, spin Ruijs...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 213; no. 5; pp. 769 - 785
Main Author Reshetikhin, N.
Format Journal Article
LanguageEnglish
Published New York Springer US 04.03.2016
Springer
Subjects
Mathematics
Mathematics and Statistics
Modulus Space
Poisson Algebra
Conjugacy Class
Poisson Structure
Coadjoint Orbit
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-016-2738-9

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Summary:The subject of this paper is degenerate integrability in Hamiltonian mechanics. We start with a short survey of degenerate integrability. The first section contains basic notions. It is followed by a number of examples which include the Kepler system, Casimir models, spin Calogero models, spin Ruijsenaars models, and integrable models on symplectic leaves of Poisson Lie groups. The new results are degenerate integrability of relativistic spin Ruijsenaars and Calogero–Moser systems and the duality between them. Bibliography: 30 titles.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-016-2738-9