A bounded sequence of bitransitive and capture Sierpiński curve Julia sets for 3-circle inversions
Volume 262 / 2023
Fundamenta Mathematicae 262 (2023), 205-220
MSC: Primary 37F10; Secondary 37F20, 37F45.
DOI: 10.4064/fm166-4-2023
Published online: 28 June 2023
Abstract
We demonstrate the existence of a bounded sequence of infinitely many parameter values for $3$-circle inversion that lead to Sierpiński curve Julia sets. This sequence consists of alternating parameter values that, although they all yield Sierpiński curves, are distinguished by the behavior of their critical points and are not dynamically conjugate.
