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Confocal surfaces and integrable billiards on the sphere and in the Lobachevsky space

✍ Scribed by Alexander P. Veselov

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
917 KB
Volume
7
Category
Article
ISSN
0393-0440

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✦ Synopsis

Billiard problems for the domains on the sphere and hyperbolic space bounded by the corresponding conical sections are investigated. It is shown that these discrete systems are integrable and correspond to the translations on the Jacobi varieties of certain hyperelliptic curves. The explicit formulas in terms of O-functions are exhibited. The consideration is based on the factorization method, developed recently by J. Moser and the author.

πŸ“œ SIMILAR VOLUMES

On the rate of quantum ergodicity on hyp
On the rate of quantum ergodicity on hyperbolic surfaces and for billiards
✍ R. Aurich; M. Taglieber πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 1001 KB

The rate of quantum ergodicity is studied for three strongly chaotic (Anosov) systems. The quantal eigenfunctions on a compact Riemannian surface of genus g ---2 and of two triangular billiards on a surface of constant negative curvature are investigated. One of the triangular billiards belongs to t