Closed almost-periodic orbits in semiclassical quantization of generic polygons

Periodic orbits are the central ingredients of modem semiclassical theories and corrections to these are generally nonclassical in origin. We show her e that, for the class of generic polygonal billiards, the corrections are p redominantly classical in origin owing to the contributions from closed alm ost-periodic (CAP) orbit families. Furthermore, CAP orbit families outnumbe r periodic families but have comparable weights. They are hence indispensab le for semiclassical quantization.