Description

• Title:
  On the chaos game of iterated function systems
• Creator:
  Barrientos, Pablo G.;
  Ghane, Fatemeh H.;
  Malicet, Dominique;
  Sarizadeh, Aliasghar
• Description:
  Every quasi-attractor of an iterated function system (\rom{IFS}) of continuous functions on a first-countable Hausdorff topological space is renderable by the probabilistic chaos game. By contrast, we prove that the backward minimality is a necessary condition to get the deterministic chaos game. As a consequence, we obtain that an \rom{IFS} of homeomorphisms of the circle is renderable by the deterministic chaos game if and only if it is forward and backward minimal. This result provides examples of attractors (a forward but no backward minimal \rom{IFS} on the circle) that are not renderable by the deterministic chaos game. We also prove that every well-fibred quasi-attractor is renderable by the deterministic chaos game as well as quasi-attractors of both, symmetric and non-expansive \rom{IFS}s.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.10.05
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 49, No 1 (March 2017); 105 - 132;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.064/9879 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.064/9880
• Subject:
  Iterated function system;
  well-fibred attractors;
  deterministic and probabilistic chaos game;
  forward and backward minimality;
  Primary;
  37C05;
  37C20;
  Secondary;
  37E10
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.064
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other