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Birkhoff normal forms of linear systems of ordinary heromorphic differential equations

Objective

The project concerns linear systems of differential equations in the complex domain that are in, or can be transformed into, Birkhoff standard form. One line of research will be to investigate links between the Riemann-Hilbert problem and the Birkhoff problem which were stated by Bolibrukh and Balser. I also would like to carry out a possible generalization of these problems to the case of difference equations and possibly evenq-difference equations. I also want to study the solutions of equations that are in Birkhoff standard form. Of course, much is known about the behavior of solutions, even for general systems, when one considers only the point infinity, but there is more to do concerning the central connection problem, i.e. the question of how a solution with a particular form near the origin behaves at infinity. Since the Birkhoff normal form of an equation is not uniquely determined, I shall also .investigate this freedom - or in other words, try to find a precise description of which systems in Birkhoff normal form can be transformed one into the other , using either meromorphic or analytic transformations. I intend to substantially broad -knowledge in k-summability, resurgent analysis and difference equations theory by utilizing the extensive expertise of Professor Balser. This will allow me to extend my research to investigations of the Birkhoff problem and the central connection problem which are fields of interest for Professor Balser and frequently invited visitors at the University of Ulm like Professor Majima and Professor Anosov.

Coordinator

UNIVERSITY OF ULM
Address
Helmholzstrasse 18
89069 Ulm
Germany