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SUMMARY:Simon Baker (University of Birmingham)
DTSTART:20220922T161500Z
DTEND:20220922T173000Z
DTSTAMP:20260423T022144Z
UID:NEDNT/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/50/">O
 verlapping iterated function systems from the perspective of Metric Number
  Theory</a>\nby Simon Baker (University of Birmingham) as part of New Engl
 and Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstr
 act\nKhintchine’s theorem is a classical result from metric number theor
 y which relates the Lebesgue measure of certain limsup sets with the diver
 gence of naturally occurring volume sums. Importantly this result provides
  a quantitative description of how the rationals are distributed within th
 e reals. In this talk I will discuss some recent work where I prove that a
  similar Khintchine like phenomenon occurs typically within many families 
 of overlapping iterated function systems. Families of iterated function sy
 stems these results apply to include those arising from Bernoulli convolut
 ions\, the 0\,1\,3 problem\, and affine contractions with varying translat
 ion parameters. \nTime permitting I also will discuss a particular family 
 of iterated function systems for which we can be more precise. Our analysi
 s of this family shows that by studying the metric properties of limsup se
 ts\, we can distinguish between the overlapping behaviour of iterated func
 tion systems in a way that is not available to us by simply studying prope
 rties of self-similar measures.\n
LOCATION:https://researchseminars.org/talk/NEDNT/50/
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