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Conformal Geometry and Dynamics

ISSN 1088-4173



Geometry of the Feigenbaum map

Author: Xavier Buff
Journal: Conform. Geom. Dyn. 3 (1999), 79-101
MSC (1991): Primary 58F; Secondary 30D05
Published electronically: August 12, 1999
MathSciNet review: 1716570
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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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Additional Information

Xavier Buff
Affiliation: Université Paul Sabatier, Laboratoire Emile Picard, 31062 Toulouse cedex, France

Keywords: Dynamics, puzzle, renormalization, Feigenbaum, local connectivity
Received by editor(s): January 27, 1998
Received by editor(s) in revised form: May 19, 1999
Published electronically: August 12, 1999
Article copyright: © Copyright 1999 American Mathematical Society