Séminaires : Séminaire de Systèmes Dynamiques

Equipe(s) : gd,
Responsables :H. Eliasson, B. Fayad, R. Krikorian, P. Le Calvez
Email des responsables :
Salle : 15-25-502
Adresse :Campus Pierre et Marie Curie

Archive avant 2015

Hébergé par le projet Géométrie et Dynamique de l’IMJ

Orateur(s) Vadim Kaloshin - UMD & IST,
Titre Marked Length Spectrum determination of generic convex analytic domains
Horaire14:00 à 15:45
RésumeM. Kac popularized a beautiful and important question "Can you hear the shape of a drum?". Formally, for a domain Ω ? R^2 the Laplace spectrum Sp(Ω) is the collection of the eigenvalues of the Dirichlet problem for the Laplacian ∆u + ?^2 u = 0, u = 0 on ∂Ω. Does Sp(Ω) determine a domain Ω? In general, the answer is negative due to examples of Gordon-Webb-Wolpert, but the boundary in this example is neither smooth nor analytic. The (marked) length spectrum L(Ω) is a collection of lengths of all periodic orbits of the billiard inside Ω (marked by period). The Laplace spectrum generically determines the length spectrum. We show that generically (for an open dense set) the marked length spectrum L(Ω) determines an analytic strictly convex domain. Earlie Zelditch showed that in the class of axis-symmetric analytic domains the Laplace spectrum generically (for a residual set) does determine a domain. This is a joint work in progress joint with M. Leguil and K. Zhang.
AdresseCampus Pierre et Marie Curie