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Geometry of the Feigenbaum map
Author(s):
Xavier
Buff
Journal:
Conform. Geom. Dyn.
3
(1999),
79-101.
MSC (1991):
Primary 58F;
Secondary 30D05
Posted:
August 12, 1999
MathSciNet review:
1716570
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Abstract:
We show that the Cvitanovic-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.
References:
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- O.E. LANFORD A computer assisted proof of the Feigenbaum conjectures, Bull. Amer. Math.Soc., vol. 6, (1982), 427-434. MR 83g:58051
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Additional Information:
Xavier
Buff
Affiliation:
Université Paul Sabatier, Laboratoire Emile Picard, 31062 Toulouse cedex, France
DOI:
10.1090/S1088-4173-99-00031-4
PII:
S 1088-4173(99)00031-4
Keywords:
Dynamics,
puzzle,
renormalization,
Feigenbaum,
local connectivity
Received by editor(s):
January 27, 1998
Received by editor(s) in revised form:
May 19, 1999
Posted:
August 12, 1999
Copyright of article:
Copyright
1999,
American Mathematical Society
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