More Cantorvals / Більше канторвалів

Abstract: New characterizations of Cantorvals will be presented and a new family of non-multigeometric Cantorvals will be constructed allowing to answer some questions related to algebraic summation of achievable sets. It is a joint work with Jacek Marchwicki (Olsztyn) and Piotr Nowakowski (Lodz).

У доповіді буде представлено нові характеризації канторвалів і побудовано нову сім'ю немультигеометричних канторвалів, що дасть змогу відповісти на деякі запитання, пов'язані з алгебраїчним сумуванням досяжних множин. Це спільна робота з Яцеком Мархвіцким (Ольштин) і Пйотром Новаковским (Лодзь).

classical analysis and ODEsnumber theory

Audience: researchers in the discipline

( slides )

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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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