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Abstract: We prove the Feigenbaum-Coullet-Tresser conjecture on the hyperbolicity of the renormalization transformation of bounded type. This gives the first computer-free proof of the original Feigenbaum observation of the universal parameter scaling laws. We use the Hyperbolicity Theorem to prove Milnor's conjectures on self-similarity and "hairiness" of the Mandelbrot set near the corresponding parameter values. We also conclude that the set of real infinitely renormalizable quadratics of type bounded ... (Update)
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...L is transversally quasiconformal if the holonomy between any two transversals is locally qc. The lemma implies (see e.g. [L5, Appendix 2]) Corollary 2.6 (Transverse qc structure) Any holomorphic lamination is transversally quasiconformal. A holomorphic motion h :...
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BibTeX entry: (Update)
M. Lyubich, Feigenbaum-Coullet-Tresser Universality and Milnor's Hairiness Conjecture, Annals of Mathematics, to appear (1998). http://citeseer.ist.psu.edu/lyubich99feigenbaumcoullettresser.html More
@misc{ lyubich98feigenbaumcoullettresser,
author = "M. Lyubich",
title = "Feigenbaum-Coullet-Tresser Universality and Milnor's Hairiness Conjecture",
text = "M. Lyubich, Feigenbaum-Coullet-Tresser Universality and Milnor's Hairiness
Conjecture, Annals of Mathematics, to appear (1998).",
year = "1998",
url = "citeseer.ist.psu.edu/lyubich99feigenbaumcoullettresser.html" }
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