The Geometry of Integrable and Superintegrable Systems

Details The Geometry of Integrable and Superintegrable Systems The Geometry of Integrable and Superintegrable Systems

2012-03-08

arxiv.org/abs/1203.1663v1

Physics

Mathematical Physics

Scientific paper

The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical structure like symplectic, Poisson, etc. Such geometrical structure provides a generalized toroidal bundle on the carrier space of the system. Non--canonical diffeomorphisms of such structure generate alternative Hamiltonian structures for complete integrable Hamiltonian systems. The energy-period theorem provides the first non--trivial obstruction for the equivalence of integrable systems.

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