Geodesic
The Stationary Phase Method for Certain Degenerate Critical Points I
Canadian journal of mathematics, Tome 41 (1989) no. 5, pp. 907-931

Voir la notice de l'article provenant de la source Cambridge University Press

We consider, in this work, the asymptotic behaviour for large λ, of a Fourier integral where φ(x) is in general a C ∞ function and a(x) a C ∞ function with compact support. It is well known that the asymptotic behaviour of this integral is controlled by the behaviour of φ at its critical points (i.e., points where ∂φ/∂xj(x) = 0) and is given by local contributions at these points ([1], [3], [7], [9]).In general, one assumes the hypothesis of non degenerate isolated critical point, namely that the determinant of the second derivative at the critical point is non zero. 
Dostal, Milos; Gaveau, Bernard. The Stationary Phase Method for Certain Degenerate Critical Points I. Canadian journal of mathematics, Tome 41 (1989) no. 5, pp. 907-931. doi: 10.4153/CJM-1989-042-3
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