2002 Fiscal Year Final Research Report Summary
Analysis of Complex Dynamics
| Project/Area Number |
13440047
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | KYOTO UNIVERSITY |
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Principal Investigator |
TANIGUCHI M Graduate School of Science, Math., Ap, 大学院・理学研究科, 助教授 (50108974)
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| Co-Investigator(Kenkyū-buntansha) |
SHIGA H Graduate School of Sci, TIT, Math., P, 大学院・理工学研究科, 教授 (10154189)
KISAKA M Graduate School of HE, Math., Ap, 大学院・人間環境学研究科, 助教授 (70244671)
KOKUBU H Graduate School of Science, Math., Ap, 大学院・理学研究科, 助教授 (50202057)
MATSUZAKI K Fac, of Sci., Ochanomizu Univ. Math. AP, 理学部, 助教授 (80222298)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Complex dynamics / Sullivan's dictionary / entire function / Kleinian group / representation space / branched cover |
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| Research Abstract |
The head investigator, M. Taniguchi introduced a new kind of combinatorial model for the covering structure of an entire function, which is called "a configuration tree". This concept is the counterpart of that of the Cayley graph of a Kleinian group in the context of the Sullivan's dictionary.
This new model enabled us to find a very important class of entire functions, which is called the class of structurally finite entire functions. We also discovered that every element of this class has the very explicit representation as a primitive function of a decorated exponential function. As a consequence, we also proved that the Julia set of every structurally finite entire function has the Hausdorff dimension two.
Furthermore, very recently we proved the Bell conjecture on explicit representation of multi-connected planar domains affirmatively by using the Hurwitz space, which is a kind of the representation space of holomorphic branched covering structures.
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