منابع مشابه
On nonconvex caustics of convex billiards
Oliver Knill July 29, 1996 Abstract There are billiard tables of constant width, for which the billiard map has invariant curves in the phase space which belong to continuous but nowhere di erentiable caustics. We apply this to construct ruled surfaces which have a nowhere di erentiable lines of striction. We use it also to get Riemannian metrics on the sphere such that the caustic belonging at...
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We begin the study of billiard dynamics in Finsler geometry. We deduce the Finsler billiard reflection law from the “least action principle”, and extend the basic properties of Riemannian and Euclidean billiards to the Finsler and Minkowski settings, respectively. We prove that the Finsler billiard map is a symplectomorphism, and compute the mean free path of the Finsler billiard ball. For the ...
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Caustics are curves with the property that a billiard trajectory, once tangent to it, stays tangent after every reflection at the boundary of the billiard table. When the billiard table is an ellipse, any nonsingular billiard trajectory has a caustic, which can be either a confocal ellipse or a confocal hyperbola. Resonant caustics —the ones whose tangent trajectories are closed polygons— are d...
متن کاملCaustics of de Sitter spacelike curves in Minkowski 3-space
In this paper, we consider evolutes of spacelike curves in de Sitter 2-space. Applying the theory of singularity theory, we find that these evolutes can be seen as one dimensional caustics which are locally diffeomorphic to lines or ordinary cusps. We establish the relationships between singularities of caustics and geometric invariants of curves under the action of the Lorentz group. c ©2016 A...
متن کاملSpectral Duality for Planar Billiards
ao -d yn /9 40 50 01 2 M ay 1 99 4 Spectral Duality for Planar Billiards J.-P. Eckmann1;2 and C.-A. Pillet1 Dépt. de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland Section de Mathématiques, Université de Genève, CH-1211 Genève 4, Switzerland Abstract. For a bounded open domain with connected complement in R2 and piecewise smooth boundary, we consider the Dirichlet Lapla...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2018
ISSN: 0951-7715,1361-6544
DOI: 10.1088/1361-6544/aa9d5c