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

Graeme Boore, Kenneth John Falconer

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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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.
Original languageEnglish
Pages (from-to)325-349
Number of pages24
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume154
Issue number02
Early online date31 Oct 2012
DOIs
Publication statusPublished - 2013

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