A note on Diophantine-type fractals for \alpha-L\"uroth systems
Sara Munday
TL;DR
This paper investigates the Hausdorff dimensions of specific sets of real numbers defined via -Lruth expansions, contributing to the understanding of fractal structures in number theory.
Contribution
It provides new results on the Hausdorff dimensions of Diophantine-type fractals associated with -Lruth systems, a novel application in fractal geometry and number theory.
Findings
Determined Hausdorff dimensions for certain -Lruth fractal sets
Established relationships between -Lruth expansions and fractal dimensions
Extended understanding of fractal structures in Diophantine approximation
Abstract
The Hausdorff dimensions of certain sets of real numbers described in terms of the \alpha-L\"uroth expansion are given.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Topological and Geometric Data Analysis · advanced mathematical theories