中科院数学与系统科学研究院

数学研究所

动力系统研讨班报告

报告人：Prof. Walter Bergweiler(University of Kiel, Germany)

题  目：Quasiconformal surgery and linear differential equations

时  间：2019.11.14（星期四）, 16:00-17:00

地  点：数学院南楼N224室

摘  要：We consider the frequency of zeros of solutions of the differential equation  w′′+Aw=0  with an entire coefficient A. First we review the results for a polynomial coefficient A. Next we discuss various results due to Bank, Laine and others dealing with the case that A is a transcendental entire function. We then describe a new method to construct coefficients A for which there are two linearly independent solutions with relatively few zeros. We start with certain coefficients A for which the solutions can be given explicitly and then sketch how solutions for different coefficients can be “glued” using quasiconformal maps. The method yields the solution of a problem posed by Bank and Laine. This is joint work with Alexandre Eremenko.