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Finite geometries and diffractive orbits in isospectral billiards

Olivier Giraud
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Abstract

Several examples of pairs of isospectral planar domains have been produced in the two-dimensional Euclidean space by various methods. We show that all these examples rely on the symmetry between points and blocks in finite projective spaces; from the properties of these spaces, one can derive a relation between Green functions as well as a relation between diffractive orbits in isospectral billiards.

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Olivier Giraud. 2005-03-31. Finite geometries and diffractive orbits in isospectral billiards. https://doi.org/10.1088/0305-4470%2F38%2F27%2Fl01

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