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Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure

Published online by Cambridge University Press:  31 October 2012

G. C. BOORE  and
K. J. FALCONER
G. C. BOORE
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland. e-mail: graemeb@libero.it, kjf@st-andrews.ac.uk
K. J. FALCONER
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland. e-mail: graemeb@libero.it, kjf@st-andrews.ac.uk
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Abstract

For directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 154 , Issue 2 , March 2013 , pp. 325 - 349
Copyright
Copyright © Cambridge Philosophical Society 2012

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