Billiards in Polygons
نویسندگان
چکیده
منابع مشابه
Ergodicity of Billiards in Polygons with Pockets
The billiard in a polygon is not always ergodic and never K-mixing or Bernoulli. Here we consider billiard tables by attaching disks to each vertex of an arbitrary simply connected, convex polygon. We show that the billiard on such a table is ergodic, K-mixing and Bernoulli.
متن کاملDual Billiards, Fagnano Orbits, and Regular Polygons
In this article we consider the dual version of two results on polygonal billiards. We begin by describing these original results. The first result is about the dynamics of the so-called pedal map related to billiards in a triangle P . The three altitudes of P intersect the opposite sides (or their extensions) in three points called the feet. These three points form the vertices of a new triang...
متن کاملOuter Billiards with Contraction: Regular Polygons
We study outer billiards with contraction outside regular polygons. For regular n-gons with n = 3, 4, 5, 6, 8, and 12, we show that as the contraction rate approaches 1, dynamics of the system converges, in a certain sense, to that of the usual outer billiards map. These are precisely the values of n ≥ 3 with [Q(e) : Q] ≤ 2. Then we discuss how such convergence may fail in the case of n = 7.
متن کاملOn configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards
The classical billiard system describes the motion of a point in a plane domain subject to the elastic reflection off the boundary, described by the familiar law of geometrical optics: the angle of incidence equals the angle of reflection; see, e.g., [13, 14] for surveys of mathematical billiards. For every n ≥ 2, the billiard system inside a circle has a very special property: every point of t...
متن کاملStickiness in mushroom billiards.
We investigate the dynamical properties of chaotic trajectories in mushroom billiards. These billiards present a well-defined simple border between a single regular region and a single chaotic component. We find that the stickiness of chaotic trajectories near the border of the regular region occurs through an infinite number of marginally unstable periodic orbits. These orbits have zero measur...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1978
ISSN: 0091-1798
DOI: 10.1214/aop/1176995475