This article is cited in 1 paper

Globally superintegrable Hamiltonian systems

A. Kurov, G. A. Sardanashvily

Lomonosov Moscow State University, Moscow, Russia

Abstract: 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.

Keywords: completely integrable system, superintegrable system, action–angle variable, centrally symmetric potential, Kepler system.

Received: 12.05.2016
Revised: 20.06.2016

DOI: 10.4213/tmf9225

 English version: Theoretical and Mathematical Physics, 2017, 191:3, 811–826

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