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SUMMARY:Oleh Makarchuk (Institute of Mathematics\, Natl. Acad. Sci. Ukrain
 e)
DTSTART:20250206T133000Z
DTEND:20250206T150000Z
DTSTAMP:20260423T004755Z
UID:fran/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/fran/61/">On
  some metric and probabilistic results for the $A_2$-continued fraction re
 presentation of real numbers</a>\nby Oleh Makarchuk (Institute of Mathemat
 ics\, Natl. Acad. Sci. Ukraine) as part of Семінар з фракта
 льного аналізу / Fractal analysis seminar\n\n\nAbstract\nIn t
 his talk\, we consider the $A_2$-continued fraction representation with al
 phabet $\\{\\alpha_1\, \\alpha_2\\}$ ($0 < \\alpha_1 < \\alpha_2$\, $\\alp
 ha_1 \\alpha_2 = \\frac{1}{2}$) for numbers of interval $[\\alpha_1\, \\al
 pha_2]$. We obtain metric results for this representation that are analogo
 us to the results of A. Khinchin and P. Lévy for the classical continued 
 fraction representation. The Lebesgue structure of the random variable wit
 h independent digits of its $A_2$-continued fraction representation is stu
 died.\n
LOCATION:https://researchseminars.org/talk/fran/61/
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