The problem of the determination of the Hausdorff dimension of sets via the special class of
coverings generated by special partitions, called Q*-partitions, of the unit interval is …

We introduce the conflict interaction with two positions between a couple of image
probability measures and consider the associated dynamical system. We prove the …

The distribution of a random variable ξ= 2− kτk, where τk are independent random variables
taking values 0, 1, 2 with probabilities pik, i= 0, 1, 2, is investigated. The behavior of the …

We analyze correlations between different approaches to the definition of the Hausdorff
dimension of singular probability measures on the basis of fractal analysis of essential …

We examine measure preserving mappings $ f $ acting from a probability space $(\Omega,
F,\mu) $ into a probability space $%(\Omega^{*}, F^{*},\mu^{*}), $ where $\mu^{*}=\mu (f …

The paper is devoted to the study of connections between fractal properties of one-
dimensional singularly continuous probability measures and the preservation of the …

We study the spectral properties of the limiting measures in the conflict dynamical systems
modeling the alternative interaction between opponents. It has been established that typical …

We focus on the multifractal generalization of the centered Hausdorff measure and
dimension. We analyze the correlation among different approaches to the definition of the …

AQ− representation of real numbers is introduced as a generalization of the p− adic and Q−
representations. It is shown that the Q− representation may be used as a convenient tool for …

Formulas are given for the Lebesgue measure and the Hausdorff–Besicovitch dimension of
the minimal closed set Sξ supporting the distribution of the random variable ξ= ∑^∞_k=1 2 …