This article is cited in 1 paper

Uniform Boundedness of Iterates of Analytic Mappings Implies Linearization: a Simple Proof and Extensions

Rafael de la Llave

Georgia Institute of Technology, School of Mathematics, 686 Cherry St., Atlanta GA 30332-0160, USA

Abstract: A well-known result in complex dynamics shows that if the iterates of an analytic map are uniformly bounded in a complex domain, then the map is analytically conjugate to a linear map. We present a simple proof of this result in any dimension. We also present several generalizations and relations to other results in the literature.

Keywords: analytic maps, linearization.

MSC: 30D05, 37F50, 39-02

Received: 11.09.2017
Accepted: 08.10.2017

Language: English

DOI: 10.1134/S156035471801001X

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