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...
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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 کاملFagnano Orbits of Polygonal Dual Billiards
Given a convex n-gon P , a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P . For which polygons P does the ratio Area Q/AreaP have the minimal value? The answer is shown to be: for affine-regular polygons. Mathematics Subject Classification (1991): 52-XX.
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...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2017
ISSN: 0024-6093
DOI: 10.1112/blms.12011