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BEGIN:VEVENT
UID:20200528T174406CEST-0039PiS7V7@ical.php
DTSTAMP:20200528T150506Z
CLASS:PUBLIC
DESCRIPTION:\n\n\nAbstract:\nQuestions about the stability of a fixed point
$z_0$ of an analytic map $f$ in complex dynamics are closely connected to
properties of the multiplier $\lambda = f'(z_0)$. Particularly interestin
g and difficult is the case of an irrationally indifferent fixed point\, w
here $\lambda = e^{2\pi i \alpha}$ is on the unit circle with irrational r
otation number $\alpha$. In this case\, answers depend very much on number
-theoretic properties of the rotation number\, and several questions remai
n open.\n\nIn this talk I will present applications of a beautiful classic
al result from complex analysis\, the Hadamard three-circle theorem\, to t
his question\, a technique which was first used by Hubert Cremer in 1948 i
n the context of dynamics of entire functions.\n\nThis talk will be access
ible to graduate students with a background in basic complex analysis\, an
d one of the aims is to advertise the power of some classical complex anal
ysis results which are typically not taught in the standard graduate class
es.\n\n\n
DTSTART:20181001T160000
DTEND:20181001T170000
LOCATION:Wilson Hall\, 1-144
SUMMARY:Math Sem: Lukas Geyer (MSU)\, Stability of indifferent fixed points
and the Hadamard 3-circle theorem
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