منابع مشابه
Homotopical rigidity of polygonal billiards
Consider two k-gons P and Q. We say that the billiard flows in P and Q are homotopically equivalent if the set of conjugacy classes in the fundamental group of P which contain a periodic billiard orbit agrees with the analogous set for Q. We study this equivalence relationship and compare it to the equivalence relations, order equivalence and code equivalence, introduced in [BT1, BT2]. In parti...
متن کاملOn Chaotic Dynamics in Rational Polygonal Billiards
We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular motion in polygons is taken within the alternative deterministic and stochastic frameworks. The analysis is developed in terms of the billiard-wall collision...
متن کاملInfinite Genus Surfaces and Irrational Polygonal Billiards
We prove that the natural invariant surface associated with the billiard game on an irrational polygonal table is homeomorphic to the Loch Ness monster, that is, the only orientable infinite genus real topological surface with exactly one end.
متن کاملDistribution of Husimi zeros in polygonal billiards.
The zeros of the Husimi function provide a minimal description of individual quantum eigenstates and their distribution is of considerable interest. We provide here a numerical study for pseudointegrable billiards which suggests that the zeros tend to diffuse over phase space in a manner reminiscent of chaotic systems but nevertheless contain a subtle signature of pseudointegrability. We also f...
متن کاملComplexity and Growth for Polygonal Billiards
We establish a relationship between the word complexity and the number of generalized diagonals for a polygonal billiard. We conclude that in the rational case the complexity function has cubic upper and lower bounds. In the tiling case the complexity has cubic asymptotic growth.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2012
ISSN: 0166-8641
DOI: 10.1016/j.topol.2011.09.007