Backward Iteration Algorithms for Julia sets of Möbius Semigroups

Abstract

We extend a result regarding the Random Backward Iteration algorithm for drawing Julia sets (known to work for certain rational semigroups containing a non-Möbius element) to a class of Möbius semigroups which includes certain settings not yet been dealt with in the literature, namely, when the Julia set is not a thick attractor in the sense given in [David Fried, Sebastian. M. Marotta, and Rich Stankewitz, Complex dynamics of Möbius semigroups, Ergodic Theory Dynam. Systems, 32(6):1889--1929, 2012].

Published in Discrete and Continuous Dynamical Systems Ser. A, 36, 2016, 6475 - 6485. see also http://rstankewitz.iweb.bsu.edu//, http://www.math.sci.osaka-u.ac.jp/~sumi/. arXiv admin note: text overlap with arXiv:1312.1457