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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

Abstract

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.

Keywords

Hamiltonian System Resonance System Simple Proof Homology Group Integral Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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