Diffractive orbits in isospectral billiards

Details Diffractive orbits in isospectral billiards Diffractive orbits in isospectral billiards

2003-12-19

arxiv.org/abs/nlin/0312045v1

Nonlinear Sciences

Chaotic Dynamics

20 pages, 6 figures

Scientific paper

10.1088/0305-4470/37/7/016

Isospectral domains are non-isometric regions of space for which the spectra of the Laplace-Beltrami operator coincide. In the two-dimensional Euclidean space, instances of such domains have been given. It has been proved for these examples that the length spectrum, that is the set of the lengths of all periodic trajectories, coincides as well. However there is no one-to-one correspondence between the diffractive trajectories. It will be shown here how the diffractive contributions to the Green functions match nevertheless in a ''one-to-three'' correspondence.

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