2 papers
math.DS2024
Elliptic non-degeneracy and spectral rigidity of classical billiards
Georgi Popov, Peter Topalov
In this paper we show that the billiard ball map of the Liouville billiard tables of classical type on the ellipsoid is non-degenerate at the elliptic fixed point. As a corollary w…
math.DS2009
On the Integral Geometry of Liouville Billiard Tables
G. Popov, P. Topalov
The notion of a Radon transform is introduced for completely integrable billiard tables. In the case of Liouville billiard tables of dimension 3 we prove that the Radon transform i…