A remark on expanding maps

Chang, Kung Ching; Li, Shu Jie

doi:10.1090/S0002-9939-1982-0660608-4

A remark on expanding maps
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by Kung Ching Chang and Shu Jie Li

Proc. Amer. Math. Soc. 85 (1982), 583-586

DOI: https://doi.org/10.1090/S0002-9939-1982-0660608-4

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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.

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