Journal of Applied Mathematics
Volume 2013 (2013), Article ID 868725, 9 pages
Research Article

Affine Differential Invariants of Functions on the Plane

College of Information Science and Engineering, Northeastern University, Shenyang 110004, China

Received 20 January 2013; Accepted 21 May 2013

Academic Editor: Asghar Qadir

Copyright © 2013 Yuanbin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A differential invariant is a function defined on the jet space of functions that remains the same under a group action. It is an important concept to solve the equivalence problem. This paper presents an effective method to derive a special type of affine differential invariants. Given some functions defined on the plane and an affine group acting on the plane, there are induced actions of the group on the functions and on the derivative functions of the functions. Affine differential invariants of these functions are useful in many applications. However, there has been little systematic study of this problem at present. No clear and simple results are available for application users to use directly. We propose a direct and simple method to construct affine differential invariants in this situation. Some useful explicit formulas of affine differential invariants of 2D functions are presented.