The semiclassical Einstein-Brillouin Keller vortex tube quantization for the quasi-energies in time-periodic Hamiltonians is studied for typical systems, when the vortex tubes of the quantizing tubes may have complicated structures in extended phase space. Numerical application to a periodically driven Duffing (quartic) oscillator yields semiclassical quasi-energies in excellent agreement with the exact quantum mechanical ones for the regular states.
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Bensch et al. (1992) studied this question.
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