Singularities of the wave trace near cluster points of the length spectrum

Yves Colin de Verdière (1) , Victor Guillemin (2) , David Jerison (2)

1 IF - Institut Fourier
2 MIT - Massachusetts Institute of Technology

Let h(t) be the trace of the Green function of the wave equation in the unit disk with Dirichlet boundary conditions. It is known that h(t) is smooth in the interval 2\pi < t < 8. We show that h(t) is smooth at 2\pi from the right.

Mots clés: Fonctions de Airy; Spectre du laplacien; Géodésiques périodiques; Fonctions de Bessel; Fonctions de Airy.

Domaines: Physique mathématique [math-ph]

Yves Colin de Verdière, Victor Guillemin, David Jerison. Singularities of the wave trace near cluster points of the length spectrum. 2011. ⟨hal-00551705⟩