id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-40	Chicone, Carmen; Swanson, Richard	Linearization via the Lie derivative	2000	64	.pdf	application/pdf	6752	285	65	= 0, • the partial derivatives Fx and Fy are Lipschitz in Ω, and • the partial derivative Fz is Lipschitz in Ωxy uniformly with respect to z ∈ Ωz and Hölder in Ωz uniformly with respect to (x, y) ∈ Ωxy with Hölder exponent µ. System (3.6) satisfies the (1, µ) spectral gap condition if (1 + µ)c < b. We will show that system (3.6) can be linearized by a C1 near-identity trans- formation of the form u = x+ α(x, y, z), v = y + β(x, y, z), w = z. (3.8) The proof of this result is given in three main steps: an invariant manifold theorem for a system with a spectral gap is used to find a preliminary near- identity C1 map, as in display (3.8), that transforms system (3.6) into a system of the same form but with the new function F = (f, g) “flattened” along the coordinate subspace corresponding to the invariant manifold. Equivalently, the identity Dγ(z)Cz −Aγ(z) = F (γ(z), z) (3.12) holds for all z in the domain of γ.	cache/ejde-40.pdf	txt/ejde-40.txt