2002 Fiscal Year Final Research Report Summary
RESEARCH OF A SPACE OF MEROMORPHIC MAPPINGS AND DEFICIENCIES
| 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)
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| Project Period (FY) |
2000 – 2002
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| Keywords | value distribution theory / meromorphic mapping / defect / unicity theorem / function space / complex dynamical system / dynamical system for chaos / Julia set |
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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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Research Products
(12 results)
