Probabilistic approximation of partly filled-in composite Julia sets
Volume 119 / 2017
Annales Polonici Mathematici 119 (2017), 203-220
MSC: Primary 32H50, 32U35, 37F10; Secondary 28A80, 65C05.
DOI: 10.4064/ap4100-8-2017
Published online: 26 September 2017
Abstract
We study properties of the metric space of pluriregular sets and of contractions on that space induced by finite families of proper polynomial mappings of several complex variables. In particular, we show that closed balls in the space of pluriregular sets do not have to be compact and we give a simple proof of applicability of the so-called chaos game in the case of composite Julia sets. Part of the construction of those sets also leads to a computationally viable approximation by simpler sets based on Monte-Carlo simulation.
