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Story of the Feigenbaum point

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Story of the Feigenbaum point
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27
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CC Attribution - NonCommercial - NoDerivatives 2.0 Generic:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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The Feigenbaum point is a remarkable parameter in the quadratic family focusing some of the deepest phenomena of non-linear dynamics (regular vs chaotic behavior, rigidity and MLC, universal self-similarity and renormalization). A theory of this point has been under construction for about 45 years. I will outline this story, completing it with one missing piece, MLC at this point (based on a joint work with Dima Dudko).