Open AccessAffine Differential Invariants of Functions on the Plane
Author(s) -
Yuanbin Wang,
Xingwei Wang,
Bin Zhang
Publication year - 2013
Publication title -
journal of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.307
H-Index - 43
eISSN - 1687-0042
pISSN - 1110-757X
DOI - 10.1155/2013/868725
Subject(s) - affine transformation , mathematics , affine coordinate system , differential (mechanical device) , affine space , affine combination , invariant (physics) , equivalence (formal languages) , pure mathematics , affine geometry , affine hull , affine plane (incidence geometry) , affine geometry of curves , simple (philosophy) , plane curve , physics , philosophy , epistemology , mathematical physics , thermodynamics
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
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