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

Kenneth Falconer; Tom Kempton

doi:10.1017/etds.2016.74

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

Kenneth Falconer, Tom Kempton

Pure Mathematics

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

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.

Original language	English
Pages (from-to)	1369-1388
Number of pages	20
Journal	Ergodic Theory and Dynamical Systems
Volume	38
Issue number	4
Early online date	20 Oct 2016
DOIs	https://doi.org/10.1017/etds.2016.74
Publication status	Published - Jun 2018

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10.1017/etds.2016.74

LyapunovDimension33
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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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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AB - 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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Planar self-affine sets with equal Hausdorff, box and affinity dimensions

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Non-conformal repellers: Fractal and multifractal structure of non-conformal repellers

Kenneth Falconer

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

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Non-conformal repellers: Fractal and multifractal structure of non-conformal repellers

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Kenneth Falconer

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