Assouad Dimensions and Lower Dimensions of Some Moran Sets

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 equ...

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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2020-09, Vol.2020 (2020), p.1-5
Main Author: Xiao, JiaQing
Format: Article
Language:English
Subjects:
Compression ratio
Fractals
Mathematics
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Summary: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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2020/8353591