Hereditarily non uniformly perfect non-autonomous Julia sets
Hereditarily non uniformly perfect non-autonomous Julia sets
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DOI：
10.3934/dcds.2020002
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发表时间：
2018-10
影响因子：
1.1
通讯作者：
M. Comerford;Rich Stankewitz;Hiroki Sumi
中科院分区：
文献类型：
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作者：
M. Comerford;Rich Stankewitz;Hiroki Sumi
遗传非一致完美（HNUP）集是由Stankewitz，Sugawa和Sumi在[19]中引入的，他们给出了基于Cantor集结构的几个例子。我们展示了一类例子，在非自治迭代，其中一个认为是在一般允许变化的序列的多项式组成。特别是，我们给出了一个尖锐的标准，当朱莉娅集从我们的类将HNUP，我们表明，最大可能的Hausdorff维数\开始{document}$1 $\end{document}这些朱莉娅集可以达到。后者的证明将Julia集视为非自治共形迭代函数系统的极限集，并且我们使用Rempe-Gillen和Urbánski [15]在论文中给出的Bowen公式计算Hausdorff维数。
Hereditarily non uniformly perfect (HNUP) sets were introduced by Stankewitz, Sugawa, and Sumi in [19] who gave several examples of such sets based on Cantor set-like constructions using nested intervals. We exhibit a class of examples in non-autonomous iteration where one considers compositions of polynomials from a sequence which is in general allowed to vary. In particular, we give a sharp criterion for when Julia sets from our class will be HNUP and we show that the maximum possible Hausdorff dimension of \begin{document}$ 1 $\end{document} 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 Urbánski [15].