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arXiv · 1108.2418

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

G. C. Boore·K. J. Falconer
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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.

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G. C. Boore, K. J. Falconer. 2011-08-11. Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure. https://arxiv.org/abs/1108.2418

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