 Assume that "f"(0) = 0 and that 0 is a non-degenerate critical point of "f", i.e.the second derivative D2"f"(0) defines an isomorphism of "H" with its continuous dual space "H"∗ by

Then there exists a subneighbourhood "V" of 0 in "U", a diffeomorphism "φ"