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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Geometry of the Feigenbaum map
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by Xavier Buff PDF
Conform. Geom. Dyn. 3 (1999), 79-101 Request permission

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
  • Received by editor(s): January 27, 1998
  • Received by editor(s) in revised form: May 19, 1999
  • Published electronically: August 12, 1999
  • © Copyright 1999 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 3 (1999), 79-101
  • MSC (1991): Primary 58F; Secondary 30D05
  • DOI: https://doi.org/10.1090/S1088-4173-99-00031-4
  • MathSciNet review: 1716570