On the attractor of one-dimensional infinite iterated function systems. (1st January 2013)

• Record Type: Journal Article
• Authors: Mantica, Giorgio
• Is Part Of: International journal of applied nonlinear science. Volume 1:Number 1(2013)
• Page Start: 87
• Page End: 99
• Publication Date: 2013-01-01
• Subjects: iterated function systems -- IFS -- attractors -- second generation IFS; Science -- Mathematical models -- Periodicals; Engineering -- Mathematical models -- Periodicals; Nonlinear theories -- Periodicals; 501.5118
• Languages: English
• ISSNs: 1752-2862

Abstract

We study the attractor of iterated function systems composed of infinitely many affine, homogeneous maps. In the special case of second generation IFS, defined herein, we conjecture that the attractor consists of a finite number of non-overlapping intervals. Numerical techniques are described to test this conjecture, and a partial rigorous result in this direction is proven.