Geometry of the Feigenbaum map

Details Geometry of the Feigenbaum map Geometry of the Feigenbaum map

1997-11-15

arxiv.org/abs/math/9711216v2

Mathematics

Dynamical Systems

14 pages, 7 figures

Scientific paper

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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