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Geometry of the Feigenbaum map

Xavier Buff
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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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Xavier Buff. 1998-08-11. Geometry of the Feigenbaum map. https://arxiv.org/abs/math/9711216

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