Global version of a Sternberg linearization theorem

Abstract

Let X{x) = DX(0)x + Z(x) be a smooth vector field in R[n], with X (0) = 0, such that 0 is a contracting singular point of the linear part. We aim to extend the local Sternberg theorem on the linearization of X near the origin to a global version. It is done by assuming additionally that in some coordinates the sup norm ||DZ||]R[n] is finite and sufficiently small.