The~geometry of integrable and superintegrable systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 2, pp. 264-274
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We consider the automorphism group of the geometry of an integrable system. The geometric structure used to obtain it is generated by a normal-form representation of integrable systems that is independent of any additional geometric structure like symplectic, Poisson, etc. Such a geometric structure ensures a generalized toroidal bundle on the carrier space of the system. Noncanonical diffeomorphisms of this structure generate alternative Hamiltonian structures for completely integrable Hamiltonian systems. The energy–period theorem for dynamical systems implies the first nontrivial obstruction to the equivalence of integrable systems.
Keywords:
integrable system, superintegrable system, energy–period theorem, geometric structure.
@article{TMF_2012_172_2_a6,
author = {A. Ibort and G. Marmo},
title = {The~geometry of integrable and superintegrable systems},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {264--274},
publisher = {mathdoc},
volume = {172},
number = {2},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2012_172_2_a6/}
}
A. Ibort; G. Marmo. The~geometry of integrable and superintegrable systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 172 (2012) no. 2, pp. 264-274. http://geodesic.mathdoc.fr/item/TMF_2012_172_2_a6/