Generalized exponential dichotomy and global linearization

Hartman’s linearization theorem says that if all eigenvalues of matrix A have no zero real part and f (x) is small Lipschitzian, then nonlinear system x = Ax +f (x) and its linear system x = Ax are topologically equivalent. In 1970s Palmer extended the theorem to nonautonomous systems. In this paper we extend Hartman’s theorem to the systems with generalized exponential dichotomy.  2005 Elsevier Inc. All rights reserved