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

Graeme Boore; Kenneth John Falconer

doi:10.1017/S0305004112000576

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

Graeme Boore
, Kenneth John Falconer

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	325-349
Number of pages	24
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	154
Issue number	02
Early online date	31 Oct 2012
DOIs	https://doi.org/10.1017/S0305004112000576
Publication status	Published - 2013

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10.1017/S0305004112000576

BooreFalconer
This is an author version of this article. The published version (c) Cambridge Philosophical Society 2012 is available at http://journals.cambridge.org
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http://arxiv.org/pdf/1108.2418.pdf

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title = "Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure",

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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AB - 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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DO - 10.1017/S0305004112000576

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JO - Mathematical Proceedings of the Cambridge Philosophical Society

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

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