Periodic Orbits in Polygonal Billiards

Abstract

We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation with the genus of the invariant surface. Finally, we deal with correlations in the length spectrum and find that long orbits display Poisson fluctuations.

30 pages (Latex) including 11 figures

References in corpus (1)

• Periodic Orbits and Spectral Statistics of Pseudointegrable Billiards

Cited by in corpus (10)

• Distribution of Husimi Zeroes in Polygonal Billiards
• Closed almost-periodic orbits in semiclassical quantization of generic polygons
• Effect of Boundary Conditions on Fluctuations Measures
• Semiclassical Inequivalence of Polygonalized Billiards
• Periodic orbit theory and spectral rigidity in pseudointegrable systems
• Escape from noisy intermittent repellers
• Duality between quantum and classical dynamics for integrable billiards
• Application of the Trace Formula in Pseudointegrable Systems
• Periodic orbit theory in fractal drum
• The number of perpendicularly inscribed polygons that intersect a given side in an odd sided regular polygon