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math.DS2026
From Dimension Drop to Aperiodic Order
Natalia Jurga, Dmytro Karvatskyi
We consider the parametrised family of sets for $(x,y) \in…
math.PR2026
Infinite Bernoulli convolutions generated by multigeometric series and their properties
Mykola Pratsiovytyi, Dmytro Karvatskyi, Oleg Makarchuk
The paper is devoted to infinite Bernoulli convolutions generated by positive multigeometric series and to probability distributions of random variables whose digits in an even int…
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…