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362
Obtuse Triangular Billiards II: 100 Degrees Worth of Periodic Trajectories
"... We give a rigorous computer-assisted 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 ..."
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Cited by 9 (1 self)
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We give a rigorous computer-assisted 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 one-parameter 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 ..."
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Cited by 4 (3 self)
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We consider a one-parameter 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 3-periodic 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 ..."
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ABSTRACT. We consider 3-periodic 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 J-invariant 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 ..."
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We identify all translation covers among triangular billiards surfaces. Our main tools are the J-invariant 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 n-periodic billiard trajectories in T and also estimate the number of billiard trajectories which start an ..."
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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 n-periodic 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 self-similarity phenomena in irrational triangu ..."
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Cited by 5 (1 self)
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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 self-similarity 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 step-by-step manner the cosmological bi ..."
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Cited by 20 (10 self)
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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 Hubble-normalized orthonormal frame
Results 1 - 10
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362
