منابع مشابه
Sizing Up Outer Billiard Tables
The outer billiard dynamical system models the motion of a particle around a compact domain, such as a planet orbiting a star. When considering outer billiards in hyperbolic space, an interesting problem is to determine precisely the conditions in which an orbiting particle breaks orbit and escapes to infinity. Past work has classified triangular and Penrose kite billiard tables according to wh...
متن کاملSearch Light in Billiard Tables
We investigate whether a search light, S, illuminating a tiny angle (“cone”) with vertex A inside a bounded region Q ∈ IR with the mirror boundary ∂Q, will eventually illuminate the entire region Q. It is assumed that light rays hitting the corners of Q terminate. We prove that: (I) if Q = a circle or an ellipse, then either the entire Q or an annulus between two concentric circles/confocal ell...
متن کاملOuter billiard outside regular polygons
We consider the outer billiard outside a regular convex polygon. We deal with the case of regular polygons with 3, 4, 5, 6 or 10 sides. We describe the symbolic dynamics of the map and compute the complexity of the language.
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 Lesson Learned from Outer Billiard Derivatives
As students move onward and upward through collegiate mathematics they are often impressed by the power of advanced techniques (aren’t they?), techniques allowing problems that were previously difficult or near-impossible to be solved with relative ease. For example, once students have learned the residue theorem in complex analysis they are able to elegantly evaluate integrals that were unwiel...
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: American Journal of Undergraduate Research
سال: 2011
ISSN: 1536-4585,2375-8732
DOI: 10.33697/ajur.2011.008