Assouad Dimensions and Lower Dimensions of Some Moran Sets

JiaQing Xiao and Kit C. Chan

Journal of Mathematics, 2020, vol. 2020, 1-5

Abstract: We prove that the low dimensions of a class of Moran sets coincide with their Hausdorff dimensions and obtain a formula for the lower dimensions. Subsequently, we consider some homogeneous Cantor sets which belong to Moran sets and give the counterexamples in which their Assouad dimension is not equal to their upper box dimensions and packing dimensions under the case of not satisfying the condition of the smallest compression ratio c∗>0.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8353591

DOI: 10.1155/2020/8353591

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