A simple proof of the geometric fractional monodromy theorem

A simple proof of the “geometric fractional monodromy theorem” (Broer-Efstathiou-Lukina 2010) is presented. The fractional monodromy of a Liouville integrable Hamiltonian system over a loop γ ? ?² is a generalization of the classic monodromy to the case when the Liouville foliation has singularities over γ. The “geometric fractional monodromy theorem” finds, up to an integral parameter, the fractional monodromy of systems similar to the 1: (?2) resonance system. A handy equivalent definition of fractional monodromy is presented in terms of homology groups for our proof.