One continuum class of fractal functions defined in terms of $Q_s^*$-representation of numbers

Abstract: This talk is devoted to a continuum class of functions defined in terms of a polybasic $Q_s^*$-representation of argument and value of a function. Every function in the class depends on parameter such that digits of its $s$-adic representation uniquely determine the corresponding digits of value of the function. This class contains direct proportionality with coefficient of proportionality $1$, inversor, semi-inversor, quasi-inversor, etc. Structural properties and level sets of functions are studied.

Ukrainianclassical analysis and ODEsfunctional analysisnumber theory

Audience: researchers in the discipline

Семінар з фрактального аналізу / Fractal analysis seminar

Series comments: Weekly research seminar on fractal analysis (online)

Topics:

• theory of fractals (fractal geometry and fractal analysis)
• Hausdorff–Besicovitch dimension, techniques and methods for its calculation and estimation
• functions and transformations preserving fractal (Hausdorff–Besicovitch, entropic, box-counting, packing, etc.) dimension
• sets of metric spaces that are essential for functions, sets, and dynamical systems
• self-similar, self-affine properties of mathematical objects
• systems of encoding for real numbers (numeral systems) and their applications
• metric number theory and metric theory of representations of numbers
• probabilistic number theory and probabilistic theory of representations of numbers
• measures supported on fractals, particularly singular measures and probability distributions
• nowhere monotonic and nowhere differentiable functions, functions with fractal properties
• theory of groups determined by invariants of transformations preserving tails of representation of numbers, digit frequencies, etc.

The talks are mostly in Ukrainian but English is also acceptable