Математичні об'єкти та задачі, що пов'язані з рядами Енгеля / Mathematical objects and problems related to Engel series

Abstract: У доповіді буде розглянуто математичні об'єкти, при вивченні яких виникають ряди Енгеля; задачі, що вже розв'язані стосовно рядів Енгеля; взаємозв'язки між різними модифікаціями рядів Енгеля; відкриті проблеми, що пов'язані з рядами Енгеля.

In the talk, we examine how Engel series arise in studying some mathematical objects and consider already solved problems related to Engel series, relations between various modifications of Engel series as well as open problems related to Engel series.

Ukrainianclassical analysis and ODEsnumber theoryprobability

Audience: advanced learners

---

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

---