2010 Fiscal Year Final Research Report
Studies on complex dynamics of transcendental entire functions
| Project/Area Number |
19540190
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kochi University |
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Principal Investigator |
MOROSAWA Shunsuke Kochi University, 教育研究部・自然科学系, 教授 (50220108)
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| Co-Investigator(Kenkyū-buntansha) |
TANIGUCHI Masahiko 奈良女子大学, 理学部, 教授 (50108974)
TOHGE Kazuya 金沢大学, 自然科学研究科, 准教授 (30260558)
ISHIZAKI Katsuya 日本工業大学, 工学部, 教授 (60202991)
KATO Kazuhisa 高知大学, 教育研究部・自然科学系, 教授 (20036578)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 複素解析 / 複素力学系 / 超越整関数 / 複素誤差関数 / 特異値 / 双曲成分 |
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| Research Abstract |
From the view point of the difference between dynamics of rational functions and those of transcendental entire functions, I mainly studied complex dynamics of transcendental entire functions. Singular values play important roles in studying complex dynamics. They are critical values or asymptotic values and the latter appear in the only case of transcendental entire functions. I investigated families of entire functions with two singular values and obtained some results on hyperbolic components of the parameter spaces. Furthermore, I showed a relationship between unbounded Siegel disks and asymptotic values, if transcendental entire functions have Siegel disks.
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