Results 1  10
of
362
Obtuse Triangular Billiards II: 100 Degrees Worth of Periodic Trajectories
"... We give a rigorous computerassisted proof that a triangle has a periodic billiard path provided all its angles are at most 100 degrees. One appealing thing about our proof is that the reader can use our software online to see massive visual evidence for our result and also to survey the computer pa ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
We give a rigorous computerassisted proof that a triangle has a periodic billiard path provided all its angles are at most 100 degrees. One appealing thing about our proof is that the reader can use our software online to see massive visual evidence for our result and also to survey the computer
BILLIARDS THAT SHARE A TRIANGULAR CAUSTIC
"... We consider a oneparameter family of billiard tables Tℓ which have as a common caustic the equilateral triangle γ. The billiard tables Tℓ are constructed geometrically by the string construction, where the length ℓ of the string is the parameter. We study the family of circle homeomorphisms fℓ obta ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
We consider a oneparameter family of billiard tables Tℓ which have as a common caustic the equilateral triangle γ. The billiard tables Tℓ are constructed geometrically by the string construction, where the length ℓ of the string is the parameter. We study the family of circle homeomorphisms fℓ
ON THE INCENTERS OF TRIANGULAR ORBITS IN ELLIPTIC BILLIARD
"... ABSTRACT. We consider 3periodic orbits in an elliptic billiard. Numerical experiments conducted by Dan Reznik have shown that the locus of the centers of inscribed circles of the corresponding triangles is an ellipse. We prove this fact by the complexification of the problem coupled with the comple ..."
Abstract
 Add to MetaCart
ABSTRACT. We consider 3periodic orbits in an elliptic billiard. Numerical experiments conducted by Dan Reznik have shown that the locus of the centers of inscribed circles of the corresponding triangles is an ellipse. We prove this fact by the complexification of the problem coupled
Translation Covers Among Triangular Billiards Surfaces
, 2008
"... We identify all translation covers among triangular billiards surfaces. Our main tools are the Jinvariant of Kenyon and Smillie [8] and a property of triangular billiards surfaces, which we call fingerprint type, that is invariant under balanced translation covers. 1 1 ..."
Abstract
 Add to MetaCart
We identify all translation covers among triangular billiards surfaces. Our main tools are the Jinvariant of Kenyon and Smillie [8] and a property of triangular billiards surfaces, which we call fingerprint type, that is invariant under balanced translation covers. 1 1
TOPOLOGY OF BILLIARD PROBLEMS, II
 DUKE MATHEMATICAL JOURNAL VOL. 115, NO. 3
, 2002
"... In this paper we give topological lower bounds on the number of periodic and of closed trajectories in strictly convex smooth billiards T ⊂ R m+1. Namely, for given n, we estimate the number of nperiodic billiard trajectories in T and also estimate the number of billiard trajectories which start an ..."
Abstract
 Add to MetaCart
In this paper we give topological lower bounds on the number of periodic and of closed trajectories in strictly convex smooth billiards T ⊂ R m+1. Namely, for given n, we estimate the number of nperiodic billiard trajectories in T and also estimate the number of billiard trajectories which start
Billiards in Nearly Isosceles Triangles
, 807
"... We prove that any sufficiently small perturbation of an isosceles triangle has a periodic billiard path. Our proof involves the analysis of certain infinite families of Fourier series that arise in connection with triangular billiards, and reveals some selfsimilarity phenomena in irrational triangu ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
We prove that any sufficiently small perturbation of an isosceles triangle has a periodic billiard path. Our proof involves the analysis of certain infinite families of Fourier series that arise in connection with triangular billiards, and reveals some selfsimilarity phenomena in irrational
The cosmological billiard attractor
, 2007
"... This article is devoted to a study of the asymptotic dynamics of generic solutions of the Einstein vacuum equations toward a generic spacelike singularity. Starting from fundamental assumptions about the nature of generic spacelike singularities we derive in a stepbystep manner the cosmological bi ..."
Abstract

Cited by 20 (10 self)
 Add to MetaCart
billiard conjecture: we show that the generic asymptotic dynamics of solutions is represented by (randomized) sequences of heteroclinic orbits on the ‘billiard attractor’. Our analysis rests on two pillars: (i) a dynamical systems formulation based on the conformal Hubblenormalized orthonormal frame
Results 1  10
of
362