Canonical equivalence of integrable systems, their associated (semi)- groups, and moment systems (Q1819960)

The author considers Hamiltonian systems on \({\mathbb{R}}^{2n}\). A system is defined to be integrable when the Hamiltonian is a function of the momenta only. It is shown by the construction of generating functions that any two integrable systems are equivalent. For the corresponding quantum system, a unitary transformation is constructed with maps the Hilbert spaces associated to each system onto each other. Moment systems for a Hamiltonian system are defined following \textit{P. Feinsilver} [Special functions, probability semigroups, and Hamiltonian flows (1978; Zbl 0394.33002)]. These moment systems and related semigroups introduced by Feinsilver can again be related in a canonical fashion.