On the Integral Geometry of Liouville Billiard Tables

Details On the Integral Geometry of Liouville Billiard Tables On the Integral Geometry of Liouville Billiard Tables

2009-06-02

arxiv.org/abs/0906.0451v1

Mathematics

Dynamical Systems

Scientific paper

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 $K$ 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.

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