Abstract
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.
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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.
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Aulbach, B., Garay, B.M. Linearizing the expanding part of noninvertible mappings. Z. angew. Math. Phys. 44, 469–494 (1993). https://doi.org/10.1007/BF00953663
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DOI: https://doi.org/10.1007/BF00953663