عنوان	On the chaos game of Iterated Function Systems
نوع پژوهش	مقاله چاپ‌شده در مجلات علمی
کلیدواژه‌ها	Iterated function system; well-fibred attractors; deterministic and probabilistic chaos game; forward and backward minimality
چکیده	Every quasi-attractor of an iterated function system (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 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 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 IFSs.
پژوهشگران	پابلو (نفر اول)، فاطمه قانع (نفر دوم)، ملیست (نفر سوم)، سید علی اصغر ساری زاده (نفر چهارم)