Time-independent methods in classical mechanics: Calculation of invariant tori and semiclassical energy levels via classical Van Vleck transformations

Recently introduced methods for semiclassical quantization of nonseparable systems implicitly or explicitly rely on the existence of the invariant tori of time-independent classical mechanics. We present an accelerated convergence scheme for calculation of such tori based on the classical limit of the Van Vleck transformation, and give theoretical and computational comparisons with the methods of Percival and Pomphrey, and Chapman, Garrett, and Miller.