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

DOI10.1017/S0305004112000576zbMath1290.37025arXiv1108.2418MaRDI QIDQ4911184

G. C. Boore, Kenneth J. Falconer

Publication date: 14 March 2013

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.2418

zbMATH Keywords

Hausdorff dimensionattractordirected graphIFS

Mathematics Subject Classification ID

Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Dynamical systems involving maps of the interval (37E05)

Related Items (5)

On the equality of Hausdorff measure and Hausdorff content ⋮ An application of Edelstein's contraction principle: the attractor of a graph-directed generalized iterated function system ⋮ CONTINUITY OF THE HAUSDORFF DIMENSION FOR GRAPH-DIRECTED SYSTEMS ⋮ Infinite graph-directed systems and Hausdorff dimension ⋮ Revisiting regular sequences in light of rational base numeration systems

Cites Work

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• On the structures of generating iterated function systems of Cantor sets
• Self-similar and self-affine sets: measure of the intersection of two copies
• Multifractal Decompositions of Digraph Recursive Fractals
• Exact Hausdorff measure and intervals of maximum density for Cantor sets
• Every set of finite Hausdorff measure is a countable union of sets whose Hausdorff measure and content coincide

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