Hereditarily non uniformly perfect non-autonomous Julia sets
Document Type
Article
Date of Original Version
1-1-2020
Abstract
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 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 [15].
Publication Title, e.g., Journal
Discrete and Continuous Dynamical Systems- Series A
Volume
40
Issue
1
Citation/Publisher Attribution
Comerford, Mark, Rich Stankewitz, and Hiroki Sumi. "Hereditarily non uniformly perfect non-autonomous Julia sets." Discrete and Continuous Dynamical Systems- Series A 40, 1 (2020): 33-46. doi: 10.3934/dcds.2020002.