Linearizing the expanding part of noninvertible mappings (Q1261806)

It is shown that on Banach spaces certain Lipschitz mappings of the form \((x,y)\mapsto (T(x)+ p(x,y),q(x,y))\) with linear invertible \(T\) can be transformed by homeomorphisms into mappings of the form \((x,y)\mapsto (T(x),r(x,y))\). Using this a new proof of the Hartman-Grobman theorem [see \textit{P. Hartman}, Proc. Am. Math. Soc. 14, 568-573 (1963; Zbl 0115.298)] or [\textit{U. Kirchgraber} and \textit{E. Stiefel}, `Methoden der analytischen Störungsrechnung und ihre Anwendungen', Stuttgart (1978; Zbl 0411.34050)] is given. Furthermore, some differentiability results for the pseudo-stable foliation associated to the mapping from above are given.