Доведення гіпотези Коллатца і зв'язок інтервалів на основі «тетради» / A proof of the Collatz conjecture and connection of intervals based on “tetrada”

Abstract: У доповіді обговорюється прихований «механізм» у системах числення з дробовими основами $\frac{2^a}{3}$ і $\frac{4}{3}$. Ми застосовуємо цей механізм для вивчення гіпотези Коллатца.

In the talk, a hidden “mechanism” in numeral systems with fractional bases $\frac{2^a}{3}$ and $\frac{4}{3}$ is discussed. We apply this mechanism to study the Collatz conjecture.

Ukrainiannumber theory

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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