Annales Henri Poincaré

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

Fractional Hamiltonian Monodromy

  • Nikolaií N. Nekhoroshev
  • Dmitrií A. Sadovskií
  • Boris I. Zhilinskií
Article

Abstract.

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

Keywords

Homology Group Monodromy Matrix Closed Path Skeleton Curve Oriented Component 
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

© Birkhäuser Verlag, Basel/Switzerland 2006

Authors and Affiliations

  • Nikolaií N. Nekhoroshev
    • 1
    • 2
    • 3
  • 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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