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Regular and Chaotic Dynamics

, Volume 23, Issue 1, pp 1–11 | Cite as

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

  • Rafael de la LlaveEmail author
Article

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 

MSC2010 numbers

30D05 37F50 39-02 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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