Geodesic
Superscars in the Šeba billiard
Journal of the European Mathematical Society, Tome 19 (2017) no. 10, pp. 2947-2964.

Voir la notice de l'article provenant de la source EMS Press

We consider the Laplacian with a delta potential (a “point scatterer”) on an irrational torus, where the square of the side ratio is diophantine. The eigenfunctions fall into two classes—“old” eigenfunctions (75%) of the Laplacian which vanish at the support of the delta potential, and therefore are not affected, and “new” eigenfunctions (25%) which are affected, and as a result feature a logarithmic singularity at the location of the delta potential.
DOI : 10.4171/jems/732
Classification : 81-XX, 58-XX
Keywords: Superscars, Šeba billiard, semiclassical measures 
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     title = {Superscars in the {\v{S}eba} billiard},
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Pär Kurlberg; Henrik Ueberschär. Superscars in the Šeba billiard. Journal of the European Mathematical Society, Tome 19 (2017) no. 10, pp. 2947-2964. doi : 10.4171/jems/732. http://geodesic.mathdoc.fr/articles/10.4171/jems/732/

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