On the Integral Geometry of Liouville Billiard Tables
Dynamical Systems
2009-06-03 v1 Spectral Theory
Abstract
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 is one-to-one on the space of continuous functions on the boundary which are invariant with respect to the corresponding group of symmetries. We prove also that the frequency map associated with a class of Liouville billiard tables is non-degenerate. This allows us to obtain spectral rigidity of the corresponding Laplace-Beltrami operator with Robin boundary conditions.
Keywords
Cite
@article{arxiv.0906.0451,
title = {On the Integral Geometry of Liouville Billiard Tables},
author = {G. Popov and P. Topalov},
journal= {arXiv preprint arXiv:0906.0451},
year = {2009}
}