Morse function
Let be a smooth manifold. A critical point
of a map at is called if the Hessian matrix (in any local coordinate system) at is non-degenerate.
A smooth function is called Morse if all its critical points are non-degenerate. Morse functions exist on any smooth manifold, and in fact form an open dense (http://planetmath.org/Dense) subset of smooth functions on (this fact is often phrased “a generic smooth function is Morse”).