Characteristic and Order for Polynomial Differentiability

Abstract

<p> A definition of polynomial differentiability of an arc in the real affine plane at a point is given. The differentiable points are classified with respect to the intersection and support properties of certain families of osculating polynomials. For a given point of an arc, these properties are used to define a certain n-tuple of integers, the characteristic of that point. It is shown that the polynomial order of polynomially differentiable interior point of an arc is at least as great as the sum of the digits of its characteristic.</p>