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

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

2011-08-11

arxiv.org/abs/1108.2418v1

Mathematics

Metric Geometry

Scientific paper

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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