Title: On the attractor of one-dimensional infinite iterated function systems

Authors: Giorgio Mantica

Addresses: Center for Non-linear and Complex Systems, Department of Science and High Technology, University of Insubria, 22100 Como, Italy; I.N.F.N. sezione di Milano, CNISM unitá di Como, Department of Science and High Technology, University of Insubria, 22100 Como, Italy

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.

Keywords: iterated function systems; attractors; second generation IFS; non-overlapping intervals.

DOI: 10.1504/IJANS.2013.052767

International Journal of Applied Nonlinear Science, 2013 Vol.1 No.1, pp.87 - 99

Received: 25 Oct 2012
Accepted: 25 Oct 2012
Published online: 30 Jul 2014 *

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