| Project/Area Number |
12640150
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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 | Yamagata University |
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Principal Investigator |
MORI Seiki YAMAGATA UNIV., FAC. SCI., PROFESSOR, 理学部, 教授 (80004456)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAMURA Shinzo YAMAGATA UNIV., FAC. SCI., PROFESSOR, 理学部, 教授 (50007176)
NAKADA Masami YAMAGATA UNIV., FAC. SCI., PROFESSOR, 理学部, 教授 (20007173)
TODA Nobushige NAGOYA INST. TECH., PROFESSOR EMERITUS, 名誉教授 (30004295)
AIHARA Yoshihiro NUMAZU COLL. TECH., ASSOCIATE PROFESSOR, 助教授 (60175718)
SATO Enji YAMAGATA UNIV., FAC. SCI., PROFESSOR, 理学部, 教授 (80107177)
水原 昂廣 山形大学, 理学部, 教授 (80006577)
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| Project Period (FY) |
2000 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2001: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2000: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | value distribution theory / meromorphic mapping / defect / unicity theorem / function space / complex dynamical system / dynamical system for chaos / Julia set / 有利形写像 / ネヴァンリナ理論 / 有理型写像 / 値分布論 / 測度空間 / 力学系 / 射影空間 / モーリー空間 / ウエヴレット理論 / 楕円曲線 |
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| Research Abstract |
The head investigator Mori-researched a fewness of meromorphic mappings with defects. He obtained elimination theorems of defects of hypersurfaces or rational moving targets of a meromorphic mapping into P^n(C) by a small deformation, and he also proved that mappings without defects are dense in a space of transcendental meromorphic mappings He and an investigator Aihara also obtained results that for any hypersurface of degree d on P^n(C), we can construct an algebraically nondegenerate meromorphic mapping with a preassaigned deficiency in an interval (0,α), where α 0x(3E) 0 depends only on d. An investigator Aihara obtained serveral conditions on the inverse image of a divisor under meromorphic mappings for which mappings are algebraically dependent, and he also obtained uniqueness theorems depending on the existance of defects. Toda obtained results that for a transcendental holomorphic curve f with maximaldeficiency sum in N-subgeneral position in P^n(C), there exists at least one hyperplane with δ(H, f) = 1 if N 0x(3E) n = 2m, and also exists at least N - n + 1 hyperplanes with δ(H, f) = 1 if N 0x(3E) n. Nakada investigated the ergodic theory of actions on the Julia set of a rational function and actions on the limit set of a discontinuous group of Mobius transformations. Sekigawa obtained an example of a rational function which has a Fatou component with preassinged connectivity n 【greater than or equal】 3. Kawamura found a phenomenon that a chaostic structure has a striking rule as a probablistic view point, that is, it has a convergence property of a probabilitistic density function. Sato studied the structure of the space of translation invariant operators on a Lorentz space of locally compact abelian groups. Mizuhara proved a weak decomposition theorem of Morrey functions and block functions of the Hardy space.
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