21 research outputs found
Diffractive orbits in isospectral billiards
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.Comment: 20 pages, 6 figure
Appendix: the theory of space with introduction, comments, and addenda
The epoch-making work of János Bolyai is presented here, together with a supplement outlining Hungarian political and science history to help the reader to get acquainted with the miserable fate of János Bolyai and with his intellectual world. A facsimile of a copy of Bolyai''s original 1831 Scientia Spatii (also known as the Appendix) is included, together with a translation. Comments and notes, and a survey of the effects of his work, complete the volume