Hausdorff dimensions of level sets related to moving digit means
Haibo Chen

TL;DR
This paper investigates the Hausdorff dimensions of level sets defined by lower and upper moving digit means in p-adic expansions, providing a comprehensive dimension formula for these sets based on digit mean bounds.
Contribution
It introduces the concepts of lower and upper moving digit means and determines the Hausdorff dimension of their level sets, extending understanding of digit mean dynamics in p-adic expansions.
Findings
Hausdorff dimension formulas for level sets with specified digit mean bounds
Characterization of the dimension based on the pair (α, β) within [0, p-1]
Extension of digit mean analysis to p-adic expansions
Abstract
In this paper, we will introduce and study the lower moving digit mean and the upper moving digit mean of in -adic expansion, where is an integer. Moreover, the Hausdorff dimension of level set \[B(\alpha,\beta)=\left\{x\in [0,1]\colon \underline{M}(x)=\alpha,\overline{M}(x)=\beta\right\}\] is determined for each pair of numbers and satisfying with .
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · advanced mathematical theories
