Linearizing the expanding part of noninvertible mappings

The main result of this paper is on partial linearization by means of a topological transformation of a mapping which is not supposed to be invertible. Our approach also provides a new proof (based on elementary degree theory) of the Hartman-Grobman Lemma as well as sharp results on the smoothness of the pseudo-stable foliation. The results are valid in arbitrary Banach spaces.This paper was written while the second author was an Alexander-von-Humboldt Research Fellow in the Mathematical Institute of the University of Augsburg, Germany.