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Continuity of Attractors and Invariant Measures for Iterated Function Systems

Published online by Cambridge University Press:  20 November 2018

P. M. Centore  and
E. R. Vrscay
E. R. Vrscay
Affiliation:
Department of Applied Mathematics, Faculty of Mathematics University of Waterloo Waterloo, Ontario N2L 3G1
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Abstract

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We prove the "folklore" results that both the attractor A and invariant measure μ of an N-map Iterated Function System (IFS) vary continuously with variations in the contractive IFS maps as well as the probabilities. This represents a generalization of Barnsley's result showing the continuity of attractors with respect to variations of a parameter appearing in the IFS maps. Some applications are presented, including approximations of attractors and invariant measures of nonlinear IFS, as well as some novel approximations of Julia sets for quadratic complex maps.

Keywords

Primary: 28A33secondary: 30D0558F11
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 3 , 01 September 1994 , pp. 315 - 329
Copyright
Copyright © Canadian Mathematical Society 1994

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