The Poincare-Birkhoff theorem in Quantum Mechanics
  Quantum manifestations of the dynamics around resonant tori in perturbed Hamiltonian systems, dictated by the Poincar\'e--Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number of quanta equal to the order of the classical resonance. Moreover, the associated classical phase space structures are mimicked in the quasiprobability density functions and their zeros. 
D. A. Wisniacki, M. Saraceno, F. J. Arranz, R. M. Benito, F. Borondo
nlin.CD quant-ph