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[Renormalization, equipotential annuli, and the Hausdorff measure] В. А. Тиморин |
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Аннотация: (based on a joint work with A. Blokh, G. Levin, and L. Oversteegen) For a complex single variable polynomial f of degree d, let K(f) be its filled Julia set, i.e., the union of all bounded orbits. Assume that K(f) has an invariant component K* on which f acts as a degree d*<d map. This is a simplest instance of holomorphic polynomial-like renormalization (Douady-Hubbard): the dynamics of a higher degree (degree d) polynomial f near K* can be understood in terms of a suitable lower degree (degree d*) polynomial to which the restriction of f to K* is semiconjugate. One can associate a certain Cantor-like subset G’ of the circle with K*; the latter is defined in a combinatorial way. We will describe a role the Hausdorff dimension of G’ and the respective Hausdorff measure play in geometry of K*. Язык доклада: английский Website: https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pnQT09 |
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