中科院数学与系统科学研究院
数学研究所
动力系统研究中心
学术报告会
报告人：Prof. Walter Bergweiler （Kiel University, Germany）
题 目：Hyperbolic entire functions
时 间：09.24（星期三）, 15:30--16:30
地 点：数学院南楼N202室
摘 要：
We show that an invariant Fatou component of a hyperbolic transcendental entire function is a bounded Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points and no asymptotic curves. We use this theorem to prove criteria for the boundedness of Fatou components and local connectivity of Julia sets for hyperbolic entire functions, and give examples that demonstrate that our results are optimal. A particularly strong dichotomy is obtained in the case of a function with precisely two critical values.
