Estimating the Hausdorff dimensions of univoque sets for self-similar sets
Xiu Chen, Kan Jiang, Wenxia Li
TL;DR
This paper presents a method for estimating the Hausdorff dimension of univoque sets within self-similar sets, sometimes enabling exact calculations of these dimensions.
Contribution
It introduces a novel approach to estimate and sometimes precisely determine the Hausdorff dimensions of univoque sets in self-similar structures.
Findings
Provides a new estimation method for Hausdorff dimensions.
Achieves exact dimension calculations in certain cases.
Enhances understanding of univoque sets in fractal geometry.
Abstract
An approach is given for estimating the Hausdorff dimension of the univoque set of a self-similar set. This sometimes allows us to get the exact Hausdorff dimensions of the univoque sets.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory