Geometry of the Feigenbaum map

Buff, Xavier

doi:10.1090/S1088-4173-99-00031-4

Geometry of the Feigenbaum map
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by Xavier Buff

Conform. Geom. Dyn. 3 (1999), 79-101

DOI: https://doi.org/10.1090/S1088-4173-99-00031-4

Published electronically: August 12, 1999

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Abstract:

We show that the Cvitanović-Feigenbaum 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. As a consequence, we give a combinatorial description of this ramified covering, and we show the surprising result that there exist points in the boundary of this domain with three accesses from inside the domain. Besides, there is a natural decomposition of this basin which makes it possible to recover a result of local connectivity by Hu and Jiang (The Julia set of the Feigenbaum quadratic polynomial is locally connected, Preprint, 1993) for the Feigenbaum Julia set.

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