D. Karvatskyi

activity

20232026

most citedThe achievement set of generalized multigeometric sequences

2 citations · 2 across the 7 of their papers we have counts for

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3 papers · 1 filter

math.DS2026

From Dimension Drop to Aperiodic Order

Natalia Jurga, Dmytro Karvatskyi

We consider the parametrised family of sets $E (x, y) = {n = 1 \sum \infty \frac{ε _{n}}{4 ^{n}} : (ε_{n}) \in {0, x, y, x + y}^{N}}$ for $(x,y) \in…

math.DS2026

Topological, metric and fractal properties of one family of self-similar sets

Dmytro Karvatskyi

Depending on a natural parameter $l$ , 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…