 The number is sometimes called the "order" or the "multiplicity" of the cusp, and is equal to the degree of the nonzero part of lowest degree of .These definitions have been generalized to curves defined by differentiable functions by René Thom and Vladimir Arnold, in the following way.A curve has a cusp at a point if there is a diffeomorphism of a neighborhood of the point in the ambient space, which maps the curve onto one of the above-defined cusps.