Self-similarity of the Mandelbrot set for real essentially bounded combinatorics (Q862176)
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scientific article; zbMATH DE number 5121947
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Self-similarity of the Mandelbrot set for real essentially bounded combinatorics |
scientific article; zbMATH DE number 5121947 |
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Self-similarity of the Mandelbrot set for real essentially bounded combinatorics (English)
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5 February 2007
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Let us consider a real quadratic-like germ \(f_*\) which is infinitely renormalizable with tripling essentially essential bounded combinatorics and consider the lamination given by the hybrid classes in the space of quadratic-like germs, then its holonomy map is shown to be \(C^1\) at \(f_*\) satisfies a growth condition. As a consequence a proof of the self-similarity of the Mandelbrot set for this type of combinatorics is given.
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Holomorphic dynamics
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Mandelbrot set
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Renormalization
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