Fractional monodromy in the 1:−2 resonance

We give an analytic proof of the fractional monodromy theorem for the 1:−2 oscillator system with S1 symmetry formulated by N.N. Nekhoroshev, D.A. Sadovskií, and B.I. Zhilinskií in C. R. Acad. Sci. Paris, Ser. I 335 (2002) 985–988. Our proof is based on an analytic description of the Hamiltonian flow on the fibers of the integral map of this system.