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Abstract: To study the geometry of a Fibonacci map f of even degree >= 4, Lyubich [Ly2] defined a notion of generalized renormalization, so that f is renormalizable infinitely many times. Van Strien and Nowicki [SN] proved that the generalized renormalizations R^n(f) converge to a cycle { f_1, f_2 } of order 2 depending only on l. We will explicitly relate f_1 and f_2 and show the convergence in shape of Fibonacci puzzle pieces to the Julia set of an appropriate polynomial-like map. Keywords. Holomorphic ... (Update)
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1.0: Geometry of the Feigenbaum map - Buff (1999) (Correct)
0.9: Six Lectures on Real and Complex Dynamics - Lyubich (Correct)
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BibTeX entry: (Update)
@article{ buff-fibonacci,
author = "Xavier Buff",
title = "Fibonacci Fixed Point of Renormalization",
journal = "Ergodic Theory and Dynamical Systems",
number = 20,
pages = "1287--1317",
year = 2000,
url = "citeseer.ist.psu.edu/buff00fibonacci.html" }
Citations (may not include all citations):66 Iterated Maps on the Interval as Dynamical Systems (context) - Collet, Eckmann - 1980
43 One dimensional dynamics (context) - de Melo, van Strien - 1993
35 Quantitative universality for a class of non-linear transfor.. (context) - Feigenbaum - 1978
33 the Dynamics of Polynomial-like Mappings (context) - Douady, Hubbard - 1985
21 The universal metric properties of non-linear transformation.. (context) - Feigenbaum - 1979
20 Dynamics of quadratic polynomials (context) - Lyubich - 1997
18 Local Connectivity of Julia Sets and Bifurcation Loci : Thre.. (context) - Hubbard - 1993
17 Feigenbaum-Coullet-Tresser universality and Milnor's Hairine.. - Lyubich - 1999
16 Renormalization and 3-manifolds which bers over the circle (context) - McMullen - 1996
15 Local Connectivity of Julia Sets : Expository Lectures - Milnor - 1992
12 Universal properties of maps on an interval (context) - Collet, Eckmann - 1980
11 Annals of Math Studies (context) - McMullen, Dynamics - 1994
11 The unimodal Fibonacci map (context) - Lyubich, Milnor - 1993
10 eration d'endomorphismes et groupe de renormalisation (context) - Coullet, Tresser - 1978
10 A complete proof of the Feigenbaum conjectures (context) - Eckmann, Wittwer - 1987
10 Adam Hilger Ltd (context) - Cvitanovi, Universality - 1984
8 Fixed points of composition operators II (context) - Epstein - 1989
7 the Lebesgue measure of the Julia set of a quadratic polynom.. (context) - Lyubich - 1991
5 Part II: Patterns and Parapatterns (context) - Branner, Hubbard et al. - 1992
4 Feigenbaum universality and the thermodynamical formalism (context) - Vul, Sinai et al. - 1984
4 Polynomial maps with a Julia set of positive Lebesgue measur.. (context) - van Strien, Nowicki - 1994
2 Renormalization Ideas in Conformal Dynamics - Lyubich - 1995
2 Fixed points of the period-doubling operator (context) - Epstein - 1992
2 Aspects of renormalization in dynamical systems theory (context) - Tresser - 1995
1 Keller - Some remarks on recent results about S-unimodal map.. (context) - Hofbauer - 1990
1 Geometry of the Feigenbaum xed point of renormalization (context) - Buff - 1999
1 Ensembles de Julia de mesure strictement positive (context) - Buff - 1996
1 Points xes de renormalisation (context) - Buff - 1996
1 van Strien - Absorbing Cantor sets in dynamical systems : Fi.. (context) - Bruin, Keller et al. - 1994
1 Institute for Mathematical Sciences (context) - Lyubich, uller et al. - 1993
1 Regular and stochastic dynamics in the real quadratic family (context) - Lyubich - 1998
Documents on the same site (http://borel.ups-tlse.fr/~buff/Preprints/Preprints.html): More
Scaling ratios and triangles in Siegel disks. - Buff, Henriksen (1998) (Correct)
Julia Sets in Parameter Spaces. - Buff, Henriksen (Correct)
Geometry of the Feigenbaum map - Buff (1999) (Correct)
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