1999/06/10 by Giorgio Mantica, Jan Ove R. Ebbestad, Anette S. Högström +1 · 1 citation
Computer Science · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Algorithm #Archaeology #Artificial intelligence #Cellular Automata and Applications #Chaotic #Computer science #Dynamical billiards #Geography #Geology #Geometry #Integrable system #Mathematical Dynamics and Fractals #Mathematics #Ordovician #Paleontology #Paleontology and Stratigraphy of Fossils #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum mechanics #Scaling #Semiclassical physics #chao-dyn #nlin.CD
paper · pdf · doi:10.1103/physreve.61.6434
11 pages, 5 figures
arxiv created 1999/06/10 · openalex publication_date 2009/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/06/11
We study the algorithmic complexity of motions in classical polygonal billiards, which, as the number of sides increases, tend to curved billiards, both regular and chaotic. This study unveils the equivalence of this problem to the procedure of quantization: the average complexity of symbolic trajectories in polygonal billiards features the same scaling relations (with respect to the number of sides) that govern quantum systems when a semiclassical parameter is varied. Two cases, the polygonal approximations of the circle and of the stadium, are examined in detail and are presented as paradigms of quantization of integrable and chaotic systems.