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.