A Computer-assisted Proof of the Feigenbaum Conjectures
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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...
متن کاملFeigenbaum - Coullet - Tresser universality and Milnor ’
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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In this paper we present a computer{assisted proof of the existence of a solution for the Feigenbaum equation '(x) = 1 '('( x)): There exist by now various such proofs in the literature. Although the one presented here is new, the main purpose of this paper is not to provide yet another version, but to give an easy{to{read and self contained introduction to the technique of computer{assisted pr...
متن کاملPeriod Doubling in Area-Preserving Maps: An Associated One Dimensional Problem
It has been observed that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of R. A renormalization approach has been used in a computer-assisted proof of existence of an area-preserving map with orbits of all binary periods in [EKW1] and [EKW2]. As it is the case with all non-trivial universality problems in non-dissipative systems in...
متن کاملDynamics of the Universal Area-preserving Map Associated with Period Doubling: Stable Sets
It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of R. A renormalization approach has been used in (Eckmann et al 1982) and (Eckmann et al 1984) in a computer-assisted proof of existence of a “universal” areapreserving map F∗ — a map with orbits of all binary periods 2 , k ∈ N. In this paper, we consider infinitely re...
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