Only ellipsoids have caustics

DOI10.1007/BF01460986zbMath0847.34052MaRDI QIDQ1907186

Peter M. Gruber

Publication date: 8 October 1996

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165364

zbMATH Keywords

ellipsoidsconvex causticscaustics of billiard tables

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Dynamical systems and ergodic theory (37-XX)

Related Items (11)

Sections and projections of nested convex bodies ⋮ Gutkin billiard tables in higher dimensions and rigidity ⋮ Arnold diffusion in multidimensional convex billiards ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ Duality of caustics in Minkowski billiards ⋮ Characterization of ellipsoids and polarity in convex sets ⋮ Classification of symmetric periodic trajectories in ellipsoidal billiards ⋮ On nonconvex caustics of convex billiards ⋮ Billiard characterization of spheres ⋮ Open problems on billiards and geometric optics ⋮ Inverse problems and rigidity questions in billiard dynamics

Cites Work

• Convex billiards
• Characterizations of ellipsoids
• Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki
• Unsolved problems in geometry
• On the second differentiability of convex surfaces
• Seules les quadriques admettent des caustiques
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