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Planar self-affine sets with equal Hausdorff, box and affinity dimensions

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Author(s)

Kenneth Falconer, Tom Kempton

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Abstract

Using methods from ergodic theory along with properties of the Furstenberg measure we obtain conditions under which certain classes of plane self-affine sets have Hausdorff or box-counting dimensions equal to their affinity dimension. We exhibit some new specific classes of self-affine sets for which these dimensions are equal.
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Original languageEnglish
Pages (from-to)1369-1388
Number of pages20
JournalErgodic Theory and Dynamical Systems
Volume38
Issue number4
Early online date20 Oct 2016
DOIs
Publication statusPublished - Jun 2018

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