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TMF, 2012, Volume 172, Number 2, Pages 264–274 (Mi tmf6955)  

The geometry of integrable and superintegrable systems

A. Ibortab, G. Marmob

a Departamento de Matemáticas, Universidad Carlos III de Madrid, Madrid, Spain
b Dipartimento di Scienze Fisiche, Università di Napoli "Federico II", Napoli, Italia

Abstract: 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

DOI: https://doi.org/10.4213/tmf6955

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English version:
Theoretical and Mathematical Physics, 2012, 172:2, 1109–1117

Bibliographic databases:


Citation: A. Ibort, G. Marmo, “The geometry of integrable and superintegrable systems”, TMF, 172:2 (2012), 264–274; Theoret. and Math. Phys., 172:2 (2012), 1109–1117

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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