Assouad dimensions of Moran sets and Cantor-like sets
wen-wen Li, wen-xia Li, jun-jie Miao, li-feng Xi
TL;DR
This paper investigates the Assouad dimensions of Moran and Cantor-like sets, providing new insights into their geometric complexity under certain conditions.
Contribution
It introduces methods to determine Assouad dimensions of Moran and Cantor-like sets, expanding understanding of their fractal geometry.
Findings
Assouad dimensions of Moran sets are characterized under specific conditions.
Assouad dimensions of Cantor-like sets are analyzed using homogeneous set techniques.
New bounds or formulas for dimensions are proposed.
Abstract
We obtain the Assouad dimensions of Moran sets under suitable condition. Using the homogeneous set, we also study the Assouad dimensions of Cantor-like sets.
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Taxonomy
TopicsMathematical Dynamics and Fractals