Speaker(s): Mariusz Urbański(University of North Texas)
Time: 09:00-10:00 November 4, 2022
Venue: Online
We consider the subclass of class B consisting of meromorphic functions for which infinity is not an asymptotic value and whose all poles have orders uniformly bounded from above. This class was introduced in [BwKo2012] and the Hausdorff dimension HD(I(f)) of the set I(f) of all points escaping to infinity under forward iteration of was estimated therein. In this lecture, based on joint paper with Volker Mayer, we provide a closed formula for the exact value of HD(I(f)) identifying it with the critical exponent of the natural series introduced in [BwKo2012]. This exponent is very easy to calculate for many concrete functions. In particular, we construct a function from this class which is of infinite order and for which HD(I(f))=0.
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