The geometry of integrable and superintegrable systems Articles uri icon

publication date

  • August 2012

start page

  • 1109

end page

  • 1117


  • 2


  • 172

International Standard Serial Number (ISSN)

  • 0040-5779

Electronic International Standard Serial Number (EISSN)

  • 1573-9333


  • 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.