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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 191, No. 3, pp. 389–406, June, 2017.
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Kurov, A.V., Sardanashvily, G.A. Globally superintegrable Hamiltonian systems. Theor Math Phys 191, 811–826 (2017). https://doi.org/10.1134/S0040577917060022
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DOI: https://doi.org/10.1134/S0040577917060022