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• W2897744297 abstract "Hereditarily non uniformly perfect (HNUP) sets were introduced by Stankewitz, Sugawa, and Sumi in cite{SSS} who gave several examples of such sets based on Cantor set-like constructions using nested intervals. We exhibit a class of examples in non-autonomous iteration where one considers compositions of polynomials from a sequence which is in general allowed to vary. In particular, we give a sharp criterion for when Julia sets from our class will be HNUP and we show that the maximum possible Hausdorff dimension of $1$ for these Julia sets can be attained. The proof of the latter considers the Julia set as the limit set of a non-autonomous conformal iterated function system and we calculate the Hausdorff dimension using a version of Bowen's formula given in the paper by Rempe-Gillen and Urb'{a}nski cite{RU}." @default.
• W2897744297 created "2018-10-26" @default.
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• W2897744297 date "2018-10-09" @default.
• W2897744297 modified "2023-09-23" @default.
• W2897744297 title "Hereditarily non Uniformly Perfect non-Autonomous Julia Sets" @default.
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• W2897744297 doi "https://doi.org/10.48550/arxiv.1810.04229" @default.
• W2897744297 hasPublicationYear "2018" @default.
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