Annales Henri Poincaré

, Volume 7, Issue 6, pp 1099–1211 | Cite as

Fractional Hamiltonian Monodromy

  • Nikolaií N. NekhoroshevEmail author
  • Dmitrií A. Sadovskií
  • Boris I. Zhilinskií


We introduce fractional monodromy in order to characterize certain non-isolated critical values of the energy–momentum map of integrable Hamiltonian dynamical systems represented by nonlinear resonant two-dimensional oscillators. We give the formal mathematical definition of fractional monodromy, which is a generalization of the definition of monodromy used by other authors before. We prove that the 1:( − 2) resonant oscillator system has monodromy matrix with half-integer coefficients and discuss manifestations of this monodromy in quantum systems.

Communicated by Eduard Zehnder


Homology Group Monodromy Matrix Closed Path Skeleton Curve Oriented Component 
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Copyright information

© Birkhäuser Verlag, Basel/Switzerland 2006

Authors and Affiliations

  • Nikolaií N. Nekhoroshev
    • 1
    • 2
    • 3
    Email author
  • Dmitrií A. Sadovskií
    • 1
  • Boris I. Zhilinskií
    • 1
  1. 1.UMR 8101 du CNRSUniversité du LittoralDunkerqueFrance
  2. 2.Department of Mathematics and MechanicsMoscow State UniversityMoscowRussia
  3. 3.Dipartimento di Matematica “Federigo Enriques”Universita degli studi di MilanoMilanoItaly

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