Scarcity of Periodic Orbits in Outer Billiards
نویسندگان
چکیده
منابع مشابه
Research Announcement: Unbounded Orbits for Outer Billiards
In [S] we proved that the outer billiards system defined on the Penrose kite has an unbounded orbit. In this article we will sketch some of the main ideas in the proof, and describe in detail a very convincing computer demonstration of our result.
متن کاملPeriodic Orbits in Outer Billiard
It is shown that the set of 4-period orbits in outer billiard with piecewise smooth convex boundary has an empty interior, provided the boundary is not a parallelogram.
متن کاملA proof of Culter’s theorem on the existence of periodic orbits in polygonal outer billiards
We prove a recent theorem by C. Culter: every polygonal outer billiard in the affine plane has a periodic trajectory. This note contains a proof of a recent theorem by Chris Culter; he obtained this result as an undergraduate participant of the 2004 Penn State REU program. A complete account of Culter’s work involving a more general class of maps and a more detailed analysis of their periodic o...
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 کاملPeriodic orbits and semiclassical form factor in barrier billiards
Using heuristic arguments based on the trace formulas, we analytically calculate the semiclassical two-point correlation form factor for a family of rectangular billiards with a barrier of height irrational with respect to the side of the billiard and located at any rational position p/q from the side. To do this, we first obtain the asymptotic density of lengths for each family of periodic orb...
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: The Journal of Geometric Analysis
سال: 2017
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-017-9927-8