NARROW-TUBE APPROXIMATION OF SEMICLASSICAL QUASI-ENERGIES - APPLICATION TO THE WEAKLY NONLINEAR DUFFING OSCILLATOR

An exact transformation of semiclassical quantization conditions determining quantal quasi-energies of time-periodic Hamiltonian systems is suggested. For motion on vortex tubes centred at stable periodic orbits the classical quasi-energy of the underlying periodic orbit separates out as a single term which is a lower bound for the quantized quasi-energies. A particular approximation involving the classical Lewis invariant for calculating semiclassical quasi-energies near the centre of a perturbed linear response is discussed in some detail.