MetaCartSign in to MyCiteSeer

Include Citations | Advanced Search | Help

Include Citations | Advanced Search | Help

  Liouville billiard tables and an inverse spectral result G.Popov and P.Topalov

Download:
Download as a PDF | Download as a PS
unknown authors
http://www.ma.utexas.edu/mp_arc/c/02/02-182.ps.gz
Add To MetaCart

Abstract:

We consider a class of billiard tables (X; g), where X is a smooth compact manifold of dimension 2 with smooth boundary @X and g is a smooth Riemannian metric on X, the billiard ow of which is completely integrable. The billiard table (X; g) is dened by means of a special double cover with two branched points and it admits a group of isometries G = Z 2 Z 2. Its boundary can be characterized by the string property, namely, the sum of distances from any point of

Citations

5 Spectral invariants of convex planar regions – Marvizi, Melrose - 1982
4 R.Melrose: The Poisson summation formula for manifolds with boundary – Guillemin - 1979
4 The billiard ball problem on a table with convex boundary - an illustrative dynamical problem – Poritsky - 1950
2 An inverse spectral result for elliptical regions – Guillemin, Melrose - 1979
2 Panoramas et Syntheses, Societe Mathematique de – Tabachnikov, Billiards - 1995
2 Confocal surfaces and integrable billiards on the sphere and in the Lobachevsky space – Veselov - 1990
1 Integrable billiards on surfaces of constant curvature – Bolotin
1 A.Fomenko: Integrable geodesic on two dimensional surfaces – Bolsinov - 2000
1 Billiard systems on quadric surfaces and the Poncelet theorem – Chang, Shi - 1989
1 Kalliterakis: Integrable curvilinear billiards, Phys – Drizzi, Grammaticos, et al.
1 ormander: The Analysis of Linear Partial – H - 1985
1 Geodesic on two-dimensional manifolds with an additional integral that is polynomial with respect to velocities (Russian – Kolokol'tsov
1 Topalov: Geodesic equivalence of metrics on surfaces as integrability, Dokl – Matveev, P
1 Invariants of the length spectrum and spectral invariants for convex planar domains – Popov - 1994
View or Download | Add to My Collection | Correct Errors