Analytic transformations of complex manifolds

复流形的解析变换

• 批准号: 04640154
• 负责人: UEDA Tetsuo
• 金额: $ 1.41万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04640154/
• 关键词: Complex dynamics; Fatou set; Critically finite map; Kobayashi hyperbolicity; ジュリア集合; 楕円関数; 超吸引的不動点; 安定多様体; ケーラー多様体; ドルボー補題; L^2コホモロジー

We investigeted complex dynamical system defind by holo-morphic maps of a complex projective space onto itself, as a generalization of the iteration theory of rational function of one complex variable.The Fatou set is defined to be the maximal open set on which the family of the iterates of such a holomorphic map constitute a normal family. This is considered as one of the most fundamental object in the theory. In our study we have proved that the Fatou set os pseudoconvex and hence a Stain open set, and further that follows that, every basin of attraction of an attracting periodic point or that of parabolic periodic point contains a critical point.We have also given some examples of dynamical systems ori pro-jective planes for which the Fatou set can be concretely described using elliptic functions, and for which the Fatou set is empty.Further we studied the ralation among the Fatou set, the forward orbit of the set of the critical points and its limit set set. In particular, we stydied the critically finite case, i.e., the case for which the orbit of the the set of the critical points is an algebraic set. For the case of dimension 2, we have given the condi-tion for the Fatou set is empty.

我们通过一个复杂的投影空间的全态图来调查复杂的动力系统污染，因为一个复合变量的理性函数迭代理论的概括。FATOU集合被定义为最大的开放集，在该集合上，这种骨度图的迭代家族构成了一个正常的家族。这被认为是理论上最基本的对象之一。 In our study we have proved that the Fatou set os pseudoconvex and hence a Stain open set, and further that follows that, every basin of attraction of an attracting periodic point or that of parabolic periodic point contains a critical point.We have also given some examples of dynamical systems ori pro-jective planes for which the Fatou set can be concretely described using elliptic functions, and for which the Fatou set is empty.Further we研究了FATOU集合之间的铺设，临界点集合的正向轨道及其极限集。特别是，我们设计了非常有限的情况，即关键点集合的轨道是代数集。对于尺寸2的情况，我们给了FATOU集的条件是空的。

项目成果

UEDA, Tetsuo: "Fatou sets in complex dynamics on projective spaces" J.Math.Soc.Japan. (to appear).

UEDA，Tetsuo：“Fatou 在射影空间上设置了复杂的动力学”J.Math.Soc.Japan。

森本芳則: "Estimates for degenarate Schrodinger operators and hypoellipticity for infinitely degenerate elliptic operators" J.Math.Kyoto Univ.32. 333-372 (1992)

Yoshinori Morimoto：“简并薛定谔算子的估计和无限简并椭圆算子的亚椭圆性”J.Math.Kyoto Univ.32 (1992)。

宇敷 重廣: "Boettcher´s theorem and super-stable marifolds for multedemensiovral complex dynamicalstystems" Advanced Series in Dynanrical Systems. 10. (1993)

Shigehiro Ushiki：“Boettcher 定理和多维复杂动力系统的超稳定万向节”动态系统高级系列 10。（1993 年）

MORIMOTO,Yoshinori: "Hypoelliptic operators of principal type with infinite degeneracy" Tukuba J.Math.(to appear). 19 (1994)

MORIMOTO、Yoshinori：“具有无限简并性的主类型的亚椭圆算子”Tukuba J.Math.（即将出现）。

MORIMOTO,Yoshinori: "Some remarks on hypo-elliptic operators which are not micro-hypoelliptic" Publ.RIMS Kyoto Univ.28. 579-586 (1992)

MORIMOTO，Yoshinori：“关于非微亚椭圆算子的一些评论”Publ.RIMS京都大学28。