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We give an overview of research topics at the Department of Dynamical Systems
and Fractal Analysis. In particular, various systems of encoding (representation) for
real numbers with finite and infinite alphabet are discussed. We use these systems
for analytical definition and studying some mathematical objects with complicated
local structure. Singular probability distribution functions, nowhere differentiable
functions, and nowhere monotonic functions are among them. We study fractal
properties of such functions, i.e., fractal properties of their level sets, graphs, and
other related sets.
Zoom link for lecture.