  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.
