Structurally fractal continuous functions defined in terms of infinite-symbol and Cantor representations of real numbers (presentation of the C.Sc. degree dissertation)

Abstract: This is a joint meeting of the Department of Theory of Functions seminar and the Fractal analysis seminar (Institute of Mathematics of the National Academy of Sciences of Ukraine), where the Ph.D. student will present research results obtained in the Candidate of Sciences (Ph.D.) degree dissertation and this dissertation will be discussed.

This work belongs to the theory of continuous locally complicated functions with fractal properties. The main object of the research is a continuum class of functions defined by means of a brand-new system of encoding for real numbers ($B$-representation of numbers) with a two-sided infinite alphabet (the set of integer numbers). Results on structural, topological and metric, variational, integral and differential, and fractal properties of functions of this class are presented.

The functions belonging to this class differ essentially from the functions previously studied using other representations of numbers because the two-sided infinite alphabet produces unexpected consequences.

Ukrainianclassical analysis and ODEsfunctional analysisnumber 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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