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SUMMARY:Oleh Makarchuk (Institute of Mathematics\, Natl. Acad. Sci. Ukrain
 e)
DTSTART:20241024T123000Z
DTEND:20241024T140000Z
DTSTAMP:20260423T004729Z
UID:fran/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/fran/55/">An
  analog of the Gauss–Kuzmin problem for $A_2$-continued fractions</a>\nb
 y Oleh Makarchuk (Institute of Mathematics\, Natl. Acad. Sci. Ukraine) as 
 part of Семінар з фрактального аналізу / Fracta
 l analysis seminar\n\n\nAbstract\nIn the talk\, the $A_2$-continued fracti
 on representation of numbers $[a_1\, a_2\, \\ldots\, a_n\, \\ldots] \\in [
 0.5\, 1]$ with alphabet $\\{0.5\, 1\\}$ is considered. For operator $T([a_
 1\, a_2\, \\ldots\, a_n\, \\ldots]) = [a_2\, a_3\, \\ldots\, a_{n+1}\, \\l
 dots]$\, we study a sequence of functions $f_n(x) = \\lambda(T^{-n}([0.5\,
  x]))$\, where $x \\in [0.5\, 1]$ and $\\lambda(\\cdot)$ is the Lebesgue m
 easure. We prove that the sequence $(f_n(x))$ converges pointwise to some 
 limiting function and analyze the asymptotics of the corresponding converg
 ence.\n
LOCATION:https://researchseminars.org/talk/fran/55/
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