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Regul. Chaotic Dyn., 2018, Volume 23, Issue 1, Pages 1–11 (Mi rcd304)  

This article is cited in 1 scientific paper (total 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

Funding Agency Grant Number
National Science Foundation DMS-1500943
The work of the author was supported in part by NSF grant DMS-1500943.


DOI: https://doi.org/10.1134/S156035471801001X

References: PDF file   HTML file

Bibliographic databases:

MSC: 30D05, 37F50, 39-02
Received: 11.09.2017
Accepted:08.10.2017
Language:

Citation: Rafael de la Llave, “Uniform Boundedness of Iterates of Analytic Mappings Implies Linearization: a Simple Proof and Extensions”, Regul. Chaotic Dyn., 23:1 (2018), 1–11

Citation in format AMSBIB
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\by Rafael de la Llave
\paper Uniform Boundedness of Iterates of Analytic Mappings Implies Linearization: a Simple Proof and Extensions
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 1
\pages 1--11
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yoshitaka Saiki, James A. Yorke, “Quasi-periodic Orbits in Siegel Disks/Balls and the Babylonian Problem”, Regul. Chaotic Dyn., 23:6 (2018), 735–750  mathnet  crossref
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