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The Siegel – Bruno Linearization Theorem

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Abstract

The purpose of this paper is a pedagogical one. We provide a short and self-contained account of Siegel’s theorem, as improved by Bruno, which states that a holomorphic map of the complex plane can be locally linearized near a fixed point under certain conditions on the multiplier. The main proof is adapted from Bruno’s work.

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Change history

  • 29 October 2023

    The numbering issue has been changed to 4-5.

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Authors and Affiliations

  1. PSL Research University, Université Paris-Dauphine, CEREMADE (UMR CNRS 7534), 75775, PARIS CEDEX 16, France

    Patrick Bernard

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  1. Patrick Bernard
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Correspondence to Patrick Bernard.

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The author declares that he has no conflicts of interest.

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MSC2010

37G05, 37F05, 37C15

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Bernard, P. The Siegel – Bruno Linearization Theorem. Regul. Chaot. Dyn. 28, 756–762 (2023). https://doi.org/10.1134/S1560354723040147

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  • DOI: https://doi.org/10.1134/S1560354723040147

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