Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure
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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.
Boore , G & Falconer , K J 2013 , ' Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure ' , Mathematical Proceedings of the Cambridge Philosophical Society , vol. 154 , no. 02 , pp. 325-349 . https://doi.org/10.1017/S0305004112000576
Mathematical Proceedings of the Cambridge Philosophical Society
This is an author version of this article. The published version (c) Cambridge Philosophical Society 2012 is available at http://journals.cambridge.org
Description"GCB was supported by an EPSRC Doctoral Training Grant whilst undertaking this work"
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