  Periodic orbit quantization requires an analytic continuation of
non-convergent semiclassical trace formulae. We propose two different methods
for semiclassical quantization. The first method is based upon the harmonic
inversion of semiclassical recurrence functions. A band-limited periodic orbit
signal is obtained by analytical frequency windowing of the periodic orbit sum.
The frequencies of the periodic orbit signal are the semiclassical eigenvalues,
and are determined by either linear predictor, Pade approximant, or signal
diagonalization. The second method is based upon the direct application of the
Pade approximant to the periodic orbit sum. The Pade approximant allows the
resummation of the, typically exponentially, divergent periodic orbit terms.
Both techniques do not depend on the existence of a symbolic dynamics, and can
be applied to bound as well as to open systems. Numerical results are presented
for two different systems with chaotic and regular classical dynamics, viz. the
three-disk scattering system and the circle billiard.

Chaotic Dynamics