  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.
