On the Integral Geometry of Liouville Billiard Tables

2009/06/02 by G. Popov, Popov, G., P. Topalov +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Spectral Theory (math.SP) #math.DS #math.SP

paper · pdf · doi:10.48550/arxiv.0906.0451

arxiv created 2009/06/02 · arxiv updated 2009/12/01

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 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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