Dendrite-type attractors of IFSs formed by two injective functions. (November 2018)

• Record Type: Journal Article
• Authors: Dumitru, Dan
• Is Part Of: Chaos, solitons and fractals. Volume 116(2018)
• Page Start: 433
• Page End: 438
• Publication Date: 2018-11
• Subjects: Attractor -- Iterated function system -- Dendrite -- Connected component; 28A80; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2018.09.031
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: The aim of this paper is to study the dendrite-type attractors of an iterated function system formed by two injective functions. We consider ( X, d ) a complete metric space and S = ( X, { f 0, f 1 }) an iterated function system (IFS), where f 0, f 1 : X ⟶ X are injective functions and A is the attractor of S . Moreover, we suppose that f 0 ( A ) ∩ f 1 ( A ) = { a } and { a } = π ( 0 m 1 ∞ ) = π ( 1 n 0 ∞ ) with m, n ≥ 1, where π is the canonical projection on the attractor. We compute the connected components of the sets A \{ π (0 ∞ )}, A \{ π (1 ∞ )}, A ∖ { π ( 0 m 1 ∞ ) = π ( 1 n 0 ∞ ) } and deduce there are infinitely-many (countably) non-homeomorphic dendrite-type attractors of iterated function systems formed by two injective functions.