Closed almost-periodic orbits in semiclassical quantization of generic polygons

Periodic orbits are the central ingredients of modern semiclassical theories and corrections to these are generally non-classical in origin. We show here that for the class of generic polygonal billiards, the corrections are predominantly classical in origin owing to the contributions from closed almost-periodic (CAP) orbit families. Furthermore, CAP orbit families outnumber periodic families but have comparable weights. They are hence indispensable for semiclassical quantization.