The Aharonov-Anandan phase of a classical dynamical system seen   mathematically as a quantum dynamical system
  It is shown that the non-adiabatic Hannay's angle of an integrable non-degenerate classical hamiltonian dynamical system may be related to the Aharonov-Anandan phase it develops when it is looked mathematically as a quantum dynamical system. 
Gavriel Segre