Several constructions in the Eremenko-Lyubich class

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• 作者：Kirill Lazebnik ^{kirill.lazebnik@stonybrook.edu}
• 关键词：Quasiconformal maps ; Wandering domains ; Entire maps ; Holomorphic dynamics
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：448
• 期：1
• 页码：611-632
• 全文大小：661 K
• 卷排序：448

文摘

We use a theorem of Bishop in [2] to construct several functions in the Eremenko–Lyubich class BB. First it is verified, that in Bishop's initial construction [2] of a wandering domain in BB, all wandering Fatou components must be bounded. Next we modify this construction to produce a function in BB with wandering domain and uncountable singular set. Finally we construct a function in BB with unbounded wandering Fatou components. It is shown that these constructions answer two questions posed in [9].