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Conformal Structures and Dynamics

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Recruitment

Vacancy Details ER position Kiel (ref 33) (filled)

(see also the vacancy on the EU CORDIS webpage)

Contract Number
035651
Core Project Title
Conformal Structures and Dynamics
Job Title
Postdoc in Dynamical Systems
Job Description

Hausdorff and Lesbesgue measure of Julia sets (task D3)

While it was shown only recently by Buff and Cheritat that there are polynomials with Julia sets of positive measure, the corresponding result for transcendental entire functions was proved already in the 1980s by Eremenko and Lyubich and by McMullen, who showed that this is the case for trigonometric functions and who also considered the Hausdorff dimension of the Julia sets of exponential functions. Since then a lot of work has been devoted to the Hausdorff dimension and area of Julia sets. Most of this work (with notable exceptions e.g. by Stallard) has been devoted to functions where the set of singular values is finite or bounded. The main tool used for functions with bounded set of singularities is a logarithmic change of variables introduced to the subject by Eremenko and Lyubich. The task would be to obtain results about Hausdorff dimension and area of Julia sets for certain classes of functions with unbounded set of singularities. Of course, here the logarithmic change of variables has to be replaced by other arguments. A condition one could pose is that the set of singularities is sufficiently "thin". Under a suitable hypothesis of this type Bargmann could prove that there are no invariant Baker domains (a result normally requiring the logarithmic change of variables). It seems possible that under hypotheses of this type one can also say something about the Hausdorff dimension and area of Julia sets. Other conditions that play a role here are suitable notions of hyperbolicity. Questions concerning the area of Julia sets are closely connected to ergodicity, and such problems are also part of the research task.

The task will be performed in Kiel (Germany) by a postdoc appointed as ER for 12 months. There will be regular contact in particular with Bremen and Göttingen and with the British, the Polish, and the Spanish team.

Contract Type
temporary
Position
Early Stage Researcher (max. 4 years of research experience)
Number of Positions
1
Deadline
15/04/2008
Start Date
01/10/2008
Duration
12 months
How to apply
Email
Contact Person

Prof Walter Bergweiler
Email: bergweiler@math.uni-kiel.de
Homepage: http://analysis.math.uni-kiel.de/bergweiler/

City
Kiel
Country
Germany
Place Of Work
Organisation City Country
University of Kiel Kiel Germany
Disciplines
Mathematics