The Hutchinson-Barnsley theory for infinite iterated function systems

By Gertruda Gwóźdź-Lukawska, Jacek R. Jachymski. Bulletin of the Australian Mathematical Society, 2005

71 citations recorded by the source corpus.

We show that some results of the Hutchinson-Barnsley theory for finite iterated function systems can be carried over to the infinite case. Namely, if {Fi : i ∈ ℕ} is a family of Matkowski's contractions on a complete metric space (X, d) such that (Fix0)i∈N is bounded for some x0 ∈ X, then there exists a non-empty bounded and separable set K which is invariant with respect to this family, that is, . Moreover, given σ ∈ ℕℕ and x ∈ X, the limit exists and does not depend on x. We also study separately the case in which (X, d) is Menger convex or compact. Finally, we answer a question posed by Máté concerning a finite iterated function system {F1,…, FN} with the property that each of Fi has a contractive fixed point.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6380843cbcac708e25011f1949565faf10712966

Citations in the corpus

• The Existence of the Attractor of Countable Iterated Function Systems (2012, unknown): “Jackymski in [8], M.”