Generalization of Hamiltonian monodromy. Quantum manifestations

Within the qualitative approach to the study of finite particle quantum systems different possible ways of the generalization of Hamiltonian monodromy are discussed. It is demonstrated how several simple integrable models like nonlinearly coupled resonant oscillators, or coupled rotators, lead to physically natural generalizations of the monodromy concept. Fractional monodromy, bidromy, and the monodromy in the case of multi-valued energy-momentum maps are briefly reviewed