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Conformal Structures and Dynamics

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Recruitment

Vacancy Details ESR position Kiel (ref 12)

(see also the vacancy on the EU CORDIS webpage)

Core Project Title
Conformal Structures and Dynamics
Salary
31710 Euros per annum plus generous mobility allowances
Job Title
Ph.D. position in Dynamical Systems
Job Description

Newton's method for entire functions (task D2)

Newton's method is a well-known algorithm of finding the zeros of a differentiable function, and its study has played a key role in the development of complex dynamics. For polynomials important results about the size and geometry of the basins of attractions have been obtained. E.g., Hubbard, Schleicher and Sutherland have shown that for a polynomial of degree d one needs at most 1.11 d (log d)^2 starting points to find all zeros. Also, the (spherical) area of the basins of attractions is bounded by c/d for some absolute constand c, provided the polynomial is suitably normalized. There are also some results about Newton's method for entire functions. E.g., Bergweiler and Terglane have shown that Sullivan's no wandering domains theorem extends to Newton's method for certain classes of entire functions, and Jankowski has considered the size and geometry of the attracting basins in some special cases. But in general much less is known about Newton's method for entire functions. The purpose of this project is to study Newton's method for much more general classes of entire functions, and to study it in greater detail for some of the classes already considered. In particular, it would be of interest to find "small" sets of starting values that find all roots. Also, it seems reasonable that the area (in the plane) of the attracting basins is infinite for functions of small order of growth. Difficulties arise in particular if the restriction of the Newton map to the immediate attracting basin is not a proper map.

The task will be performed in Kiel (Germany) by a PhD student appointed as ESR. There will be regular contact in particular with Bremen and with the Spanish team.

Contract Type
temporary
Position
Early Stage Researcher (max. 4 years of research experience)
Number of Positions
2
Deadline
31/05/2009 or until the position is filled
Start Date
As soon as possible
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