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BEGIN:VEVENT
DTSTAMP:20191007T094345Z
DTSTART:20191014T140000Z
DTEND:20191014T150000Z
SUMMARY:Thomas Jordan (Bristol) - Dimension of ergodic measures projected
onto self-similar sets
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}doe-k16fw2v
7-paad96
DESCRIPTION:Thomas Jordan (Bristol) will be speaking at this research sem
inar\, part of the Dynamical Systems and Analysis seminar series. \n\nA
bstract: Joint work with Ariel Rapaport. Self-similar sets satisfying th
e open set condition are now extremely well understood. In particular th
e dimension of any ergodic measure projected from the shift space can be
found as a ratio of entropy and Lyapunov exponent. The general case whe
re this separation is not satisfied has recently seen significant proces
s with the work of Hochman. In particular Hochman has shown that on the
line for a system where the exponential separation condition is satisfie
d the dimension of a self-similar measure (projection of a Bernoulli mea
sure from the shift space) is still given by the ratio of entropy and Ly
apunov exponent. This exponential separation condition holds for a much
wider range of sets than the open set condition (I will give examples to
show this). We will show how Hochman’s results can be extended from sel
f-similar measures to any projection of an ergodic measure. Our methods
rely on an extension of Hochman’s results on self-similar measures by Sh
merkin which gives sharp bounds on the Holder exponents of these measure
s.\n\n\n
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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