2003 Fiscal Year Final Research Report Summary
Studies on complex dynamics of transcendental entire functions and singular values
| Project/Area Number |
14540179
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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, Faculty of Science, Associate Professor, 理学部, 助教授 (50220108)
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| Co-Investigator(Kenkyū-buntansha) |
TANIGUCHI Masahiko Kyoto University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (50108974)
KATO Kazuhisa KOCHI UNIVERSITY, Faculty of Science, Professor, 理学部, 教授 (20036578)
NIIZEKI Shozo KOCHI UNIVERSITY, Faculty of Science, Professor, 理学部, 教授 (60036572)
KISAKA Masashi Kyoto University, Graduate School of Human and Environmental Studies, Associate Professor, 大学院・人間・環境学研究科, 助教授 (70244671)
THOGE Kazuya Kanazawa University, Graduate School of Natural Science and Technology, Associate Professor, 大学院・自然科学研究科, 助教授 (30260558)
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| Project Period (FY) |
2002 – 2003
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| Keywords | complex dynamics / Fatou set / Julia set / transcendental entire function / stracturally finite entire function / complex error function / wandering domain / singular value |
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| Research Abstract |
The summary of research results is as follows.
1.Morosawa and taniguchi consider dynamics of structurally finite transcendental entire functions with two singular values. In particular, they consider structurally finite transcendental entire functions with two asymptotic values, which are so-called complex error functions. They investigate hyperbolic components of the moduli space of complex error functions with real coefficients. Furthermore Morosawa proves Fatou components of certain complex error functions have a common curve in their boundaries.
2.In dynamics of polynomials, there never exist Baker domains nor wandering domains. To the contrary, in that of transcendental entire functions, there may exists those. On the other hand, any transcendental entire function can be approximated by some sequences of polynomials in the sense of locally uniformly convergence. Morosawa considers the Caratheodory convergence of Fatou sets and the Hausdorff convergence of Julia sets of such sequence
… More
s of polynomials to a certain transcendental entire function which have a Baker domain and wandering domains.
3.Taniguchi considers structurally finite transcendental entire functions and investigates their covering structure and topological structure. He defines a new kind of the deformation space of a general entire function, and discuss about completeness and stability of such deformation spaces in case of structurally finite entire functions.
5.Tohge considers unique range sets for polynomials or rational functions. He also considers related results, including (i) rational functions that share three values, and (ii) sets which are almost(apart from exceptional cases) unique range seta for different classes of meromorphic functions.
7.Kisaka constructs ray tails for structurally finite transcendental entire functions. By using these rays, he investigates topological structures for structurally finite transcendental entire functions.
8.Kisaka constructs multiply connected wandering domains by using quasi-conformal surgeries. Less
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