Affine Differential Invariants of Functions on the Plane
نویسندگان
چکیده
منابع مشابه
Affine Differential Invariants of Functions on the Plane
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...
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We show that the algebra of equi-affine differential invariants of a suitably generic surface S ⊂ R is entirely generated by the third order Pick invariant via invariant differentiation. The proof is based on the new, equivariant approach to the method of moving frames. The goal of this paper is to prove that, in three-dimensional equi-affine geometry, all higher order differential invariants o...
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Remark : An alternative approach, advocated in [4], is to use the infinitesimal invariance criteria, which requires solving a linear system of first order partial differential equations based on the prolonged infinitesimal generators of the transformation group. In contrast, the moving frame method is completely algebraic, typically much simpler, and, moreover provides significantly more inform...
متن کاملTransformation groups on real plane and their differential invariants
Complete sets of bases of differential invariants, operators of invariant differentiation and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of finite-dimensional Lie algebras on the real plane are revisited.
متن کاملEqui-affine Differential Invariants of a Pair of Curves
Let G = SAff(n, R) be the group of all transformations in R as F (x) = gx + b such that g ∈ SL(n, R) and b ∈ R. The system of generators for the differential algebra of all G-invariant differential polynomials of a pair of curves is found for the group SAff(n, R). The conditions for G-equivalence of a pair of curves is obtained.
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2013
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2013/868725