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SUMMARY:Rostyslav Kryvoshyia (Kropyvnytskyi Construction Professional Coll
 ege)
DTSTART:20240201T133000Z
DTEND:20240201T150000Z
DTSTAMP:20260423T024531Z
UID:fran/47
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/fran/47/">On
  some metric problems and structure of sequences produced by the left shif
 t operator for symbols of the $A_2$-continued fraction representation with
  alphabet $\\{0.5\, 1\\}$</a>\nby Rostyslav Kryvoshyia (Kropyvnytskyi Cons
 truction Professional College) as part of Семінар з фрактал
 ьного аналізу / Fractal analysis seminar\n\n\nAbstract\nIn the
  talk\, for a number $[a_1\, a_2\, \\ldots\, a_n\, \\ldots]$ given in term
 s of the $A_2$-continued fraction expansion with alphabet $\\{0.5\, 1\\}$\
 , we consider the left shift operator\n\\[\n  T([a_1\, a_2\, \\ldots\, a_n
 \, \\ldots]) = [a_2\, a_3\, \\ldots\, a_{n+1}\, \\ldots].\n\\]\nFor number
 s with two different $A_2$-representations we use the representation that 
 contains period $(0.5\, 1)$.\n\nLet\n\\[\n  T_n(x) = \\underbrace{T(T(\\ld
 ots T(x)))}_n.\n\\]\nWe study structure of sequences $T_n(x)$ and type of 
 the distribution corresponding to $T_n(x)$. We consider some metric result
 s for the problem when digits $\\xi_1$\, $\\xi_2$\, $\\ldots$ of the $A_2$
 -continued fraction representation of number $[\\xi_1\, \\xi_2\, \\ldots\,
  \\xi_n\, \\ldots]$ are chosen randomly and independently with probabiliti
 es $0.5$\, respectively.\n
LOCATION:https://researchseminars.org/talk/fran/47/
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