Eigenfunction Concentration for Polygonal Billiards
نویسندگان
چکیده
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 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.
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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2009
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605300902768909