Задача Гаусса–Кузьміна для різницевого представлення дійсних чисел рядами Енгеля / Gauss–Kuzmin problem for difference Engel series representation of real numbers

Abstract: Доповідь присвячена множинам дійсних чисел з $(0; 1]$, що задані умовами на їхні цифри у різницевому представленні рядами Енгеля. Зокрема, сформульовано та розв'язано задачу про різницеве представлення дійсних чисел рядами Енгеля, яка є аналогічною до задачі Гаусса–Кузьміна щодо ланцюгових дробів.

In the talk, we consider sets of real numbers from $(0, 1]$ defined by conditions on their digits of the difference Engel series representation. In particular, the so-called Gauss–Kuzmin problem for the difference Engel series representation of real numbers is introduced and solved. This is an analogue of the corresponding problem for continued fractions.

Ukrainiannumber theoryprobability

Audience: researchers in the discipline

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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

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