Euroattractor: a brief introduction to Iterated Function Systems

2002/10/30 by Karol Zyczkowski, Artur Lozinski
Physics and Astronomy · #nlin.CD

paper · pdf

published as pages 231-241 in "Simplicity behind Complexity", (ed. W. Klonowski), Pabst Publishers, Langerich, 2004. · 8 pages, 4 figures, to be published in Proceedings of the EUROATTRACTOR conference, Warsaw, June 2002

arxiv created 2002/10/30 · arxiv updated 2009/11/30

Abstract

In this work we propose a definition of an Euroattractor: an attracting invariant measure of a certain iterated functions system (IFS). An IFS is defined by specifying a set of functions, defined in subsets of R^N or in a classical phase space, which act randomly on the initial point, so it may be considered as a generalization of the notion of classical dynamical system. If the functions are sufficiently contracting, there exists an invariant measure of the system, often concentrated on a fractal set. We investigate invariant measures of a certain class of generalized or weakly contracting IFS's.

Related

• Weakly contractive iterated function systems and beyond: A manual
• Invariant measures for place dependent idempotent iterated function systems
• The Hutchinson-Barnsley theory for iterated function systems with general measures
• The R-IFSs and their attractors
• On a typical compact set as the attractor of generalized iterated\n function systems of infinite order