Globally superintegrable Hamiltonian systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 3, pp. 389-406
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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.
@article{TMF_2017_191_3_a1,
author = {A. Kurov and G. A. Sardanashvily},
title = {Globally superintegrable {Hamiltonian} systems},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {389--406},
publisher = {mathdoc},
volume = {191},
number = {3},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2017_191_3_a1/}
}
A. Kurov; G. A. Sardanashvily. Globally superintegrable Hamiltonian systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 3, pp. 389-406. http://geodesic.mathdoc.fr/item/TMF_2017_191_3_a1/