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