rectification theorem

Let U be an open subset of n and let fC1(U) be a continuousMathworldPlanetmath differentiableMathworldPlanetmathPlanetmath vector field


If there exists x0U such that f(x0)0 then there exists U0U an open neighborhood of x0 such that there exists a diffeomorphism of class C1


where V is an open subset of n such that


for all xU0 where [DF(x)] is the Jacobian of the diffeomorphism F evaluated at x and e1=(1,0,,0) is the first vector of the canonical basis of n. More generally if the vector field f is of class Cr then so is the diffeomorphism F. [AVI]


Title rectification theorem
Canonical name RectificationTheorem
Date of creation 2013-03-22 14:57:15
Last modified on 2013-03-22 14:57:15
Owner Daume (40)
Last modified by Daume (40)
Numerical id 12
Author Daume (40)
Entry type Theorem
Classification msc 34-00
Classification msc 34A12
Related topic ImplicitFunctionTheorem
Related topic TangentMap