2006 Fiscal Year Final Research Report Summary
Studies on complex dynamics of transcendental entire functions
| Project/Area Number |
17540163
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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, Professor, 理学部, 教授 (50220108)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Kazuhisa KOCHI University, Faculty of Science, Professor, 理学部, 教授 (20036578)
TANIGUCHI Masahiko Nara Women's University, Faculty of Science, Professor, 理学部, 教授 (50108974)
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)
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)
ISHIZAKI Katsuya Nippon Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (60202991)
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| Project Period (FY) |
2005 – 2006
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| Keywords | complex dynamics / transcendental entire function / complex error function / structurally finite entire / singular value / parameter space function / hyperbolic component / semihyperbolicity |
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| Research Abstract |
The summary of research results is as follows.
1. Morosawa considers dynamics of complex error functions. In particular, he studies the parameter space of those functions with real coefficients. He obtains results on parabolic bifurcations along boundaries of hyperbolic components in the parameter space.
2. Complex error functions belong to the family of the structurally finite entire functions, which is defined by Taniguchi. Structurally finite entire functions with two singular values are classified into three types; complex error functions, simply decorated exponential maps and cubic polynomials. Morosawa and Taniguchi study the hyperbolic components in the parameter space of structurally finite entire functions with two singular values. They obtain results on hyperbolic component of capture type and prepare a paper.
3. Taniguchi considers covering structure of rational functions and entire functions and those dynamical structure and studies those relationships. He also gives a model of asymptotic Teichimiiller space.
4. Tohge improves the condition on the uniqueness theorem of meromorphic functions defined in the plane. In particular, he obtains a result on a relations of two functions which comes from conditions on angular domains.
5. Kisaka constructs transcendental entire functions with doubly connected wandering domain and, more generally, those with n-multiply connected wandering domains by using improved quasiconformal surgery. He also gives a characterization on semihyperbolicity of transcendental entire functions by using orbits of singular values.
8. Ishizaki studies a relation ship between properties on solutions of the Schroder equations in value distribution theory and in theory of complex dynamics.
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Research Products
(12 results)
