The dimensions of inhomogeneous self-affine sets
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We prove that the upper box dimension of an inhomogeneous self-affine set is bounded above by the maximum of the affinity dimension and the dimension of the condensation set. In addition, we determine sufficient conditions for this upper bound to be attained, which, in part, constitutes an exploration of the capacity for the condensation set to mitigate dimension drop between the affinity dimension and the corresponding homogeneous attractor. Our work improves and unifies previous results on general inhomogeneous attractors, low-dimensional affine systems, and inhomogeneous self-affine carpets, while providing inhomogeneous analogues of Falconer’s seminal results on homogeneous self-affine sets.
Burrell , S A & Fraser , J M 2020 , ' The dimensions of inhomogeneous self-affine sets ' , Annales Academiae Scientiarum Fennicae-Mathematica , vol. 45 , no. 1 , 313-324 . https://doi.org/10.5186/aasfm.2020.4516
Annales Academiae Scientiarum Fennicae-Mathematica
Copyright © 2020 by Academia Scientiarum Fennica. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the final published version of the work, which was originally published at https://doi.org/10.5186/aasfm.2020.4516
DescriptionFunding: SAB thanks the Carnegie Trust for financially supporting this work. JMF was financially supported by a Leverhulme Trust Research Fellowship (RF-2016-500) and an EPSRC Standard Grant (EP/R015104/1).
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