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math.DS2026
Topological, metric and fractal properties of one family of self-similar sets
Dmytro Karvatskyi
Depending on a natural parameter , we study the topological, metric, and fractal properties of the homogeneous self-similar set $$K_{l}=\left\{\sum_{i=1}^{\infty} \frac{\varepsi…
math.DS2024
Fractal analysis of Guthrie-Nymann's set and its generalisations
Mykola Pratsiovytyi, Dmytro Karvatskyi
In this paper, we study the fractal properties of the boundary of the Cantorval connected with Guthrie-Nymann's series. In particular, we prove that such a Cantorval can be represe…