Moscow University Mathematics Bulletin

, Volume 68, Issue 2, pp 118–121 | Cite as

A simple proof of the geometric fractional monodromy theorem

  • D. I. Tonkonog
Brief Communications


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 ⊂ ℝ2 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.


Hamiltonian System Resonance System Simple Proof Homology Group Integral Parameter 
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© Allerton Press, Inc. 2013

Authors and Affiliations

  • D. I. Tonkonog
    • 1
  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityLeninskie Gory, MoscowRussia

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