  Fractional Hamiltonian Monodromy is a generalization of the notion of
Hamiltonian Monodromy, recently introduced by N. N. Nekhoroshev, D. A.
Sadovskii and B. I. Zhilinskii for energy-momentum maps whose image has a
particular type of non-isolated singularities. In this paper, we analyze the
notion of Fractional Hamiltonian Monodromy in terms of the Gauss-Manin
Monodromy of a Riemann surface constructed from the energy-momentum map and
associated to a loop in complex space which bypasses the line of singularities.
We also prove some propositions on Fractional Hamiltonian Monodromy for 1:-n
and m:-n resonant systems.
