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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.02107 |
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| _version_ | 1866912794631208960 |
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| author | Dudko, Dzmitry Lyubich, Mikhail |
| author_facet | Dudko, Dzmitry Lyubich, Mikhail |
| contents | We prove a priori bounds for Feigenbaum quadratic polynomials, i.e., infinitely renormalizable polynomials $f_c: z\mapsto z^2+c$ of bounded type. It implies local connectivity of the corresponding Julia sets $J(f_c)$ and MLC (local connectivity of the Mandelbrot set) at the corresponding parameters $c$. It also yields the scaling Universality, dynamical and parameter, for the corresponding combinatorics. The MLC Conjecture was open for the most classical period-doubling Feigenbaum parameter as well as for the complex tripling renormalizations. Universality for the latter was conjectured by Goldberg-Khanin-Sinai in the early 1980s. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02107 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | MLC at Feigenbaum points Dudko, Dzmitry Lyubich, Mikhail Dynamical Systems We prove a priori bounds for Feigenbaum quadratic polynomials, i.e., infinitely renormalizable polynomials $f_c: z\mapsto z^2+c$ of bounded type. It implies local connectivity of the corresponding Julia sets $J(f_c)$ and MLC (local connectivity of the Mandelbrot set) at the corresponding parameters $c$. It also yields the scaling Universality, dynamical and parameter, for the corresponding combinatorics. The MLC Conjecture was open for the most classical period-doubling Feigenbaum parameter as well as for the complex tripling renormalizations. Universality for the latter was conjectured by Goldberg-Khanin-Sinai in the early 1980s. |
| title | MLC at Feigenbaum points |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2309.02107 |