Theoretical and Mathematical Physics

, Volume 191, Issue 3, pp 811–826 | Cite as

Globally superintegrable Hamiltonian systems

  • A. V. Kurov
  • G. A. Sardanashvily


The generalization of the Mishchenko–Fomenko theorem for symplectic superintegrable systems to the case of an arbitrary, not necessarily compact, invariant submanifold allows giving a global description of a superintegrable Hamiltonian system, which can be split into several nonequivalent globally superintegrable systems on nonoverlapping open submanifolds of the symplectic phase manifold having both compact and noncompact invariant submanifolds. A typical example of such a composition of globally superintegrable systems is motion in a centrally symmetric field, in particular, the two-dimensional Kepler problem.


completely integrable system superintegrable system action–angle variable centrally symmetric potential Kepler system 


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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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