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
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Submitted: February 25, 2005; Accepted: November 17, 2005
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Nekhoroshev, N.N., Sadovskií, D.A. & Zhilinskií, B.I. Fractional Hamiltonian Monodromy. Ann. Henri Poincaré 7, 1099–1211 (2006). https://doi.org/10.1007/s00023-006-0278-4
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DOI: https://doi.org/10.1007/s00023-006-0278-4