Faithfulness and fractal equivalence principle for Perron expansions

Abstract: This talk focuses on two fundamental aspects of the fractal theory of Perron expansions. The first aspect is the faithfulness of certain families of coverings generated by Perron expansions and their applications in the Hausdorff dimension calculation. The second aspect is the fractal equivalence principle, which provides a base for the systematic transfer of fractal properties of the positive Perron expansions to their corresponding alternating expansions. We also demonstrate the applications of the fractal equivalence principle to special cases of Perron expansions, such as modified Engel expansions and Ostrogradsky–Sierpiński–Pierce expansions.

Ukrainianclassical analysis and ODEsnumber theoryprobability

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