Date of Original Version
Hereditarily non uniformly perfect (HNUP) sets were introduced by Stankewitz, Sugawa, and Sumi in  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" role="presentation">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 Urbánski .
Mark Comerford, Rich Stankewitz, Hiroki Sumi. Hereditarily non uniformly perfect non-autonomous Julia sets. Discrete & Continuous Dynamical Systems - A, 2020, 40 (1) : 33-46. doi: 10.3934/dcds.2020002
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