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CATEGORIES:Discrete Analysis Seminar
SUMMARY:Approximation on the Cantor set and other related
fractals - Demi Allen (University of Bristol)
DTSTART;TZID=Europe/London:20191120T134500
DTEND;TZID=Europe/London:20191120T144500
UID:TALK132319AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/132319
DESCRIPTION:The aim of this talk will be to consider (Diophant
ine) approximation on general ``Cantor-like'' frac
tals. In 2007\, Levesley\, Salp\, and Velani consi
dered the problem of approximating points in the m
iddle-third Cantor set at a given rate of approxim
ation by rational numbers which have denominators
which are powers of 3. They showed that the Hausdo
rff measure of the set in question is either zero
or full according to\, respectively\, the converge
nce or divergence of a certain sum which is depend
ent on the specified rate of approximation. In thi
s talk\, I will discuss an analogue of this result
for more general ``Cantor-like" fractals (specifi
cally\, for self-conformal sets satisfying the ope
n set condition). This talk is based on joint work
with Balázs Bárány (Budapest).
LOCATION:MR5\, CMS
CONTACT:Thomas Bloom
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