Principle of Stationary Phase

An asymptotic principle that the main contribution to a highly oscillatory integral ∫ a(x) e^{i k φ(x)} dx as the large parameter k → ∞ comes from neighborhoods of stationary points where φ'(x)=0 (and boundary points), with each nondegenerate stationary point contributing an explicit leading term determined by a(x), φ(x) and the Hessian of φ.