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Linearizing the expanding part of noninvertible mappings. (English) Zbl 0803.46045
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 P. Hartman, Proc. Am. Math. Soc. 14, 568-573 (1963; Zbl 0115.298)] or [U. Kirchgraber and 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.
Reviewer: A.Kriegl (Wien)

MSC:
46G05 Derivatives of functions in infinite-dimensional spaces
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