The dimensions of inhomogeneous self-affine sets
Abstract
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.
Citation
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
Publication
Annales Academiae Scientiarum Fennicae-Mathematica
Status
Peer reviewed
ISSN
1239-629XType
Journal article
Description
Funding: 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).Collections
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