Analytic transformations of complex manifolds
复流形的解析变换
基本信息
- 批准号:04640154
- 负责人:
- 金额:$ 1.41万
- 依托单位:
- 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:
- 关键词:
项目摘要
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.
作为一个复变量有理函数迭代理论的推广,研究了复射影空间到自身的全纯映射求复动力系统,定义Fatou集为这样的全纯映射族构成正规族的极大开集.这被认为是该理论中最基本的目标之一。在我们的研究中,我们证明了Fatou集是伪凸的,从而是染色开集,进而证明了吸引周期点或抛物线周期点的每个吸引盆都包含一个临界点。我们还给出了一些动力系统或射影平面的例子,其中Fatou集可以用椭圆函数来具体描述,并且Fatou集是空的。我们进一步研究了Fatou集与临界点集的前向轨道及其极限集之间的关系。特别地,我们研究了临界有限的情况,即临界点集的轨道是代数集的情况。对于2维的情形,我们给出了Fatou集为空的条件。
项目成果
期刊论文数量(48)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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)。
- DOI:
- 发表时间:
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- 影响因子:0
- 作者:
- 通讯作者:
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。
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- 影响因子:0
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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。
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- 影响因子:0
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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)。
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- 影响因子:0
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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)
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UEDA Tetsuo其他文献
UEDA Tetsuo的其他文献
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{{ truncateString('UEDA Tetsuo', 18)}}的其他基金
Fixed points and critical points in higher dimensional complex dynamics
高维复杂动力学中的不动点和临界点
- 批准号:
21540176 - 财政年份:2009
- 资助金额:
$ 1.41万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Research on Complex Dynamics
复杂动力学研究
- 批准号:
15340055 - 财政年份:2003
- 资助金额:
$ 1.41万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Solving Geometrical Puzzles by the True Slime Mold and Its Intracellular Computational Algorithm
用真正的粘菌及其胞内计算算法解决几何难题
- 批准号:
15300098 - 财政年份:2003
- 资助金额:
$ 1.41万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Emergence of intelligence by cell shape changes in a giant amoeboid cell of the true slime mold Physarum
真正的粘菌绒泡菌的巨型变形虫细胞通过细胞形状的变化而产生智慧
- 批准号:
13650266 - 财政年份:2001
- 资助金额:
$ 1.41万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Cellular Intelligence by Nonlinear Dynamics in a Slime Mold.
粘菌中非线性动力学的细胞智能。
- 批准号:
11837001 - 财政年份:1999
- 资助金额:
$ 1.41万 - 项目类别:
Grant-in-Aid for Scientific Research (C)