Planar self-affine sets with equal Hausdorff, box and affinity dimensions
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.
Citation
Falconer , K & Kempton , T 2018 , ' Planar self-affine sets with equal Hausdorff, box and affinity dimensions ' , Ergodic Theory and Dynamical Systems , vol. 38 , no. 4 , pp. 1369-1388 . https://doi.org/10.1017/etds.2016.74
Publication
Ergodic Theory and Dynamical Systems
Status
Peer reviewed
ISSN
0143-3857Type
Journal article
Rights
Copyright © 2016, Cambridge University Press. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://dx.doi.org/10.1017/etds.2016.74
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