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SUMMARY:Giulio Tiozzo (University of Toronto)
DTSTART:20210511T123000Z
DTEND:20210511T133000Z
DTSTAMP:20260423T021443Z
UID:OWNS/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/44/">Th
 e bifurcation locus for numbers of bounded type</a>\nby Giulio Tiozzo (Uni
 versity of Toronto) as part of One World Numeration seminar\n\n\nAbstract\
 nWe define a family $B(t)$ of compact subsets of the unit interval which p
 rovides a filtration of the set of numbers whose continued fraction expans
 ion has bounded digits. This generalizes to a continuous family the well-k
 nown sets of numbers whose continued fraction expansion is bounded above b
 y a fixed integer. \n\nWe study how the set $B(t)$ changes as the paramete
 r $t$ ranges in $[0\,1]$\, and describe precisely the bifurcations that oc
 cur as the parameters change. Further\, we discuss continuity properties o
 f the Hausdorff dimension of $B(t)$ and its regularity. \n\nFinally\, we e
 stablish a precise correspondence between these bifurcations and \nthe bif
 urcations for the classical family of real quadratic polynomials. \n\nJoin
 t with C. Carminati.\n
LOCATION:https://researchseminars.org/talk/OWNS/44/
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