RESEARCH OF A SPACE OF MEROMORPHIC MAPPINGS AND DEFICIENCIES

首席研究员Mori-研究了几个有缺陷的亚纯映射。他通过小变形得到了亚纯映射到P^n(C)的超曲面或有理运动目标的亏缺的消去定理，并证明了在超越亚纯映射空间中没有亏缺的映射是稠密的。他和调查者Aihara还得到了对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)上具有预亏缺的代数非退化亚纯映射，其中α0x(3e)0仅依赖于d。一个调查者Aihara得到了映射是代数依赖的亚纯映射下因子逆象的几个条件并根据缺陷的存在得到了唯一性定理。Toda得到了如下结果：对于P^n(C)中亏损和最大的超越全纯曲线f，当N0x(3e)n=2m时，至少存在一个δ(H，f)=1的超平面；当N0x(3e)n时，至少存在N-n+1个δ(H，f)=1的超平面。Sekigawa得到了一个有理函数的例子，其中Fatou分量具有预先假定的连通性n[大于或等于]3。Kawamura发现了一个现象，即混沌结构具有作为概率观点的显著规则，即它具有概率密度函数的收敛性质。Sato研究了局部紧交换群的Lorentz空间上平移不变算子空间的结构。水原证明了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.