Wave Invariants for Non-degenerate Closed Geodesics

Details Wave Invariants for Non-degenerate Closed Geodesics Wave Invariants for Non-degenerate Closed Geodesics

2000-02-04

arxiv.org/abs/math/0002037v1

Geom. Funct. Anal. 8 (1998), no. 1, 179--217

Mathematics

Spectral Theory

Scientific paper

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.

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