Euroattractor: a brief introduction to Iterated Function Systems

Details Euroattractor: a brief introduction to Iterated Function Systems Euroattractor: a brief introduction to Iterated Function Systems

2002-10-30

arxiv.org/abs/nlin/0210071v1

pages 231-241 in "Simplicity behind Complexity", (ed. W. Klonowski), Pabst Publishers, Langerich, 2004.

Nonlinear Sciences

Chaotic Dynamics

8 pages, 4 figures, to be published in Proceedings of the EUROATTRACTOR conference, Warsaw, June 2002

Scientific paper

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.

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