Wave Invariants for Non-degenerate Closed Geodesics
Steve Zelditch
Abstract
This paper generalizes the methods and results of our article xxx.lanl.gov math.SP/0002036 from elliptic to general non-degenerate closed geodesics. The main purpose is to introduce a quantum Birkhoff normal form of the Laplacian at a general non-degenerate closed geodesic in the sense of V.Guillemin. Guillemin proved that the coefficients of the normal form at an elliptic closed geodesic could be determined from the wave invariants of this geodesic. We give a new proof, and extend its range to any non-degenerate closed geodesic.
Create a lesson
Related papers
Sharp upper bounds for Steklov eigenvalues on warped products
Jade Brisson, Bruno Colbois, Alexandre Girouard et al.
Non-Bloch band theory for finite banded non-Hermitian Toeplitz matrices
Yannick de Bruijn, Erik Orvehed Hiltunen
Non-resonant angles in a Robin eigenvalue problem
Konstantin Pankrashkin
Sums of Dirichlet eigenvalues in proximity of the disk and the ball
Matthias Baur
On the inequality μ3 < λ1 for the eigenvalues of the Laplace operator
N. Filonov
Quantitative spectral stability and sharp Fourier estimates for periodic CMV matrices with decaying perturbations
Moacir Aloisio, César R. de Oliveira, Mariane Pigossi