Journal of Mathematical Sciences

, Volume 213, Issue 5, pp 769–785 | Cite as

Degenerately Integrable Systems

  • N. Reshetikhin

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.


Modulus Space Conjugacy Class Poisson Structure Poisson Algebra Coadjoint Orbit 
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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.University of AmsterdamAmsterdamThe Netherlands
  3. 3.ITMO UniversitySt.PetersburgRussia

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