Semiclassical quantization by Pade approximant to periodic orbit sums

Periodic orbit quantization requires an analytic continuation of non-conver gent semiclassical trace formulae. We propose a method for semiclassical qu antization based upon the Pade approximant to the periodic orbit sums. The Fade approximant allows the re-summation of the typically exponentially div ergent periodic orbit terms. The technique does not depend on the existence of a symbolic dynamics and can be applied to both bound and open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the three-disk scattering system and the c ircle billiard.