Localized eigenfunctions in Seba billiards

2014-08-06T12:17:24Z (GMT) by J.P. Keating J. Marklof Brian Winn
We describe some new families of quasimodes for the Laplacian perturbed by the addition of a potential formally described by a Dirac delta function. As an application, we find, under some additional hypotheses on the spectrum, subsequences of eigenfunctions of Šeba billiards that localize around a pair of unperturbed eigenfunctions.