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

作者：Boore G C^*; Falconer K J

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2013, 154(2): 325-349.

DOI：10.1017/S0305004112000576

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.

• 出版日期2013-3