A study on Fatou components of transcendental entire functions and singular values

2015 Fiscal Year Final Research Report

• Project/Area Number: 23540213
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kochi University
• Principal Investigator: Morosawa Shunsuke 高知大学, 教育研究部自然科学系理学部門, 教授 (50220108)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Keywords: 複素力学系 / 超越整関数 / 特異値 / 遊走領域 / ベーカー領域 / 力学的収束 / 広義一様収束 / ハウスドルフ収束

Outline of Final Research Achievements

I studied complex dynamics of transcendental entire functions. In particular, I investigated wandering domains and Baker domains which are Fatou components never appeared in complex dynamics of rational functions. In the case where transcendental function have those domains, the functions necessarily have infinitely many singular values. I chose a family of transcendental entire functions whose singular values are well controlled. Furthermore, some functions of the family have wandering domains or Baker domains. I gave some characterization of wandering domains and Baker domains in the family by using locally uniformly polynomial sequences.I also showed the Caratheodory convergence of components in parameter spaces.

Free Research Field

複素力学系