Feigenbaum-Coullet-Tresser Universality and Milnor's Hairiness Conjecture
نویسندگان
چکیده
منابع مشابه
Feigenbaum - Coullet - Tresser universality and Milnor ’ s Hairiness Conjecture
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 parame...
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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 parame...
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We consider a real analytic diffeomorphism ψ0 on a n-dimensional disk D, n ≥ 2, exhibiting a Feigenbaum-Coullet-Trésser (F.C.T.) attractor, being far, in the Cω(D) topology, from the standard F.C.T. map φ0 fixed by the double renormalization. We prove that ψ0 persists along a codimension-one manifold M ⊂ Cω(D), and that it is the bifurcating map along any one-parameter family in Cω(D) transvers...
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How to look at a dynamical system f at a small scale You should take a small piece of the phase space consider the rst return map to this piece and then rescale it to the original size The new dynamical system is called the renormalization Rf of the original one It may happen that Rf looks similar to f and then you can try to repeat this procedure and construct the second renormalization R f et...
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ژورنال
عنوان ژورنال: The Annals of Mathematics
سال: 1999
ISSN: 0003-486X
DOI: 10.2307/120968