RESEARCH OF A SPACE OF MEROMORPHIC MAPPINGS AND DEFICIENCIES

首席研究员mori -研究了少数带缺陷的亚纯映射。他通过小变形得到了P^n(C)亚纯映射的超曲面或理性运动目标的缺陷消除定理，并证明了在超越亚纯映射空间中没有缺陷的映射是密集的。他和研究者Aihara还得到了对于P^n(C)上的任意d次超曲面，我们可以构造一个在区间（0,α）上具有预赋缺陷的代数非退化亚纯映射。其中α 0x(3E) 0仅依赖于d。研究者Aihara在亚纯映射下，得到了映射是代数相关的除数逆像的几个条件，并得到了依赖于缺陷存在的唯一性定理。户田拓夫结果,先验的全纯曲线f maximaldeficiency N-subgeneral位置在P ^ n (C),存在至少一个超平面与δ(H f) = 1如果n 0 x (3 e) n = 2 m,至少也存在n - n + 1超平面与δ(H f) = 1如果n 0 x (3 e) n。中田宏调查行动的遍历理论的茱莉亚组有理函数和动作的限制设置不连续的默比乌斯变换。Sekigawa给出了一个具有Fatou分量的有理函数的例子，该函数的连通度为n【大于或等于】3。Kawamura发现了一种现象，即混沌结构从概率角度有一个惊人的规律，即它具有概率密度函数的收敛性。Sato研究了局部紧阿贝尔群的Lorentz空间上平移不变算子空间的结构。Mizuhara证明了Hardy空间中Morrey函数和块函数的一个弱分解定理。

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.