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SUMMARY:Daria Serhiiko (Mykhailo Drahomanov Ukrainian State University)
DTSTART:20250227T133000Z
DTEND:20250227T150000Z
DTSTAMP:20260423T004728Z
UID:fran/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/fran/64/">Th
 ree-symbol Markov representation of numbers and its applications</a>\nby D
 aria Serhiiko (Mykhailo Drahomanov Ukrainian State University) as part of 
 Семінар з фрактального аналізу / Fractal analys
 is seminar\n\n\nAbstract\nIn this talk\, we consider a three-symbol Markov
  representation of numbers in the interval $[0\, 1]$. We study topological
  and metric properties of cylinders for the Markov representation\, in par
 ticular a basic metric ratio. The notion of a Markov-normal number is intr
 oduced in terms of frequencies of digits in the representation of a number
 . An inversor of digits of the Markov representation of numbers is conside
 red. We prove that it is a continuous strictly decreasing function on the 
 interval $[0\, 1]$. Using the notion of cylindrical derivative and normal 
 properties of a number in its Markov representation we find conditions for
  the derivative of the function to be equal to zero almost everywhere with
  respect to the Lebesgue measure\, i.e.\, conditions of singularity of the
  inversor.\n
LOCATION:https://researchseminars.org/talk/fran/64/
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