First steps in symplectic and spectral theory of integrable systems (Q445206)

The paper is about the following open important general problems in classical and quantum integrable systems.NEWLINENEWLINEProblem 1. Prove that large classes of finite dimensional integrable Hamiltonian systems are characterized, up to symplectic isomorphism, by an explicit list of invariants.NEWLINENEWLINEProblem 2. Show that the semiclassical joint spectrum of a quantum integrable systems recovers the classical integrable system, up to symplectic isomorphisms.NEWLINENEWLINEA detail review of the known classification results and constructions is given. The authors discuss them and hint possible paths to arrive at a solution of the problems within an unified framework.