Geometry of the Feigenbaum map

1997/11/15 by Xavier Buff, Buff, Xavier
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematics and Applications #math.DS

paper · pdf · doi:10.48550/arxiv.math/9711216

14 pages, 7 figures

openalex publication_date 1997/11/15 · arxiv created 1998/08/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Feigenbaum-Cvitanovic equation can be interpreted as a linearizing equation, and the domain of analyticity of the Feigenbaum fixed point of renormalization as a basin of attraction. There is a natural decomposition of this basin which enables to recover a result of local connectivity by Jiang and Hu for the Feigenbaum Julia set.

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