Alternative characterizations of AGIFSs having attractor


	Open access
	Alternative characterizations of AGIFSs having attractor


	Fixed Point Theory, Volume 20, No. 2, 2019, 729-740, June 1st, 2019 DOI: 10.24193/fpt-ro.2019.2.48 Authors: Silviu-Aurelian Urziceanu Abstract: In this paper we study affine generalized iterated function systems (for short AGIFSs) which are particular cases of the concept of generalized iterated function system introduced by R. Miculescu and A. Mihail. Using a technique introduced by F. Strobin and J. Swaczyna, we associate to each n ∈ ℕ^* and each AGIFS ℱ a new AGIFS ℱ_n. Our main result states that the following statements are equivalent: a) ℱ has attractor. b) There exists n ∈ ℕ^* such that ℱ_n has attractor. c) There exists n ∈ ℕ^* such that ℱ_n is hyperbolic. d) There exists n ∈ ℕ^* such that ℱ_n is topologically contractive. Key Words and Phrases: Affine generalized iterated function system (AGIFS), attractor, hyperbolic AGIFS, topologically contractive AGIFS. 2010 Mathematics Subject Classification: 28A80, 54H20. Published on-line: June 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents