English

Backward Iteration Algorithms for Julia sets of M\"obius Semigroups

Dynamical Systems 2016-09-12 v3 Complex Variables Geometric Topology Probability

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-M\"obius element) to a class of M\"obius 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 M\"obius semigroups, Ergodic Theory Dynam. Systems, 32(6):1889--1929, 2012].

Keywords

Cite

@article{arxiv.1511.02551,
  title  = {Backward Iteration Algorithms for Julia sets of M\"obius Semigroups},
  author = {Rich Stankewitz and Hiroki Sumi},
  journal= {arXiv preprint arXiv:1511.02551},
  year   = {2016}
}

Comments

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

R2 v1 2026-06-22T11:40:09.125Z