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A remark on expanding maps


Authors: Kung Ching Chang and Shu Jie Li
Journal: Proc. Amer. Math. Soc. 85 (1982), 583-586
MSC: Primary 47H15; Secondary 58C15
DOI: https://doi.org/10.1090/S0002-9939-1982-0660608-4
MathSciNet review: 660608
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we discuss the following problem stated by L. Nirenberg: Let $ T$ be an expanding map $ H \to H$ ($ H$ is a Hilbert space) with $ T(0) = 0$. Suppose $ T$ maps a neighborhood of the origin onto a neighborhood of the origin. Does $ T$ map $ H$ onto $ H$?

We answer positively the problem when $ T$ is differentiable.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0660608-4
Keywords: Expanding map, Hadamard implicit function theorem, potential operator
Article copyright: © Copyright 1982 American Mathematical Society

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