QUANTITATIVE RESEARCH OF DEFICIENCIES OF MEROMORPFIC MAPPINGS AND EXCEPTIONAL MAPPINGS

首席研究员Mori研究了带有缺陷的亚纯映射的稀疏性。他通过小变形得到了P^n(C)亚纯映射的超曲面或有理运动目标缺陷的消去定理，并证明了无缺陷的映射在超越亚纯映射空间中是密集的。他和研究者Aihara还得到了对于P^n(C)上的任何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>0只依赖于d。Mori还研究了亚纯函数的唯一性定理。关于唯一性集的研究结果很多，但关于唯一性域的研究结果似乎很少。我们要在C中找到一个无界定义域使唯一性定理在定义域上成立。Mori， Lin和Tohge给出了限定在角域条件下的唯一性定理。研究者Aihara在亚纯映射下得到了映射代数相关的除数逆像的若干条件，并得到了两个解析分支覆盖空间相同的一个条件。这是代数函数唯一性定理的一个几何推广。Nakada研究了像有理函数一样的Blachke积的复动力学，特别是在欧几里得同余变换下的Hausdorff维数的估计和Julia集合的不变性。Sekigawa研究了作用于C的莫比乌斯变换序列的极限集，并研究了作用于一般维空间的莫比乌斯变换。他还研究了用Cliford矩阵表示莫比乌斯变换及其应用。Kawamura研究了概率密度函数的轨道，并通过计算机模拟在一组Tent映射上证明了拓扑共轭映射的一个性质。佐藤给出了雅可比正交系统与函数空间上的算子和汉克尔变换上的算子之间关系的推广。Mizuhara证明了广义Morrey空间上一个函数的弱分解定理，以及Block和Calderon-Zygmund算子。少

The head investigator Mori researched a sparsity 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>0 depends only on d. Mori also studied on uniqueness theorems of meromorphic functions. There are many results on uniqueness sets, but it seems that there are few results on uniqueness domains. We are going to find an unbounded domain in C such that a uniqueness theorem holds under the condition restricted on the domain. Mori, Lin and Tohge gave a uniqueness theorem under the condition restricted on an angular domain, an … More d the paper was submitted. An investigator Aihara obtained several conditions on the inverse image of a divisor under meromorphic mappings for which mappings are algebraically dependent, and he also obtained a condition under which two analytic ramified covering spaces are identical. This is a geometric extension of a uniqueness theorem of algebroid functions. Nakada investigated a complex dynamics of Blachke products like rational functions, especially, an estimate of a Hausdorff dimension and the invariance of Julia set under Euclidean congruent transformation. Sekigawa investigated a limit set of a sequence of Moebius transformations acting on C, and also he treated Moebius transformations acting on a general dimension space. He also studied an expression of Moebius transformations using Cliford matrix, and its applications. Kawamura studied an orbit of probabilistic density function, and also he gave a proof of a properties of topological conjugate maps on a group of Tent maps, after computer simulation. Sato gave a generalization of relation between Jacobian orthogonal system and an operators on a function space and an operators on Hankel transformations. Mizuhara proved a weak decomposition theorem related to a function on a generalized Morrey space and Block and Calderon-Zygmund operators. Less