Theoretical Study of Chaotic Phenomena

混沌现象的理论研究

• 批准号: 05452015
• 负责人: AOKI Nobuo
• 金额: $ 2.11万
• 依托单位: Tokyo Metropolitan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 1994
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05452015/
• 关键词: chaos; sensitive; manifold; dynamical system; prediction; 現象; 沈点; 源点; 環; 半群; エルゴード

Lorenz in his remarble work on the dynamical modelling of weather prediction stressed implying that some degree of uncertainty of such a prediction is unavoidable and no matter how accurate are the initial data.On the work of Lorenz it can be seen that chaotic behavior of a system with respect to initial condition was introduced in the area of dynamical systems theory. Usually, a dynamical system is given as a transformation on a space of events. This space of events can be a manifold.Concerning dynamical systems on a manifold, an interesting problem is posed as follows :"Are the diffeomorphisms with axiom A C^1-dense in the space of all surface diffeomorphisms? "Our project could give an answer for this important problem.

洛伦茨在他的remarble工作的动力学建模的天气预报强调，这意味着一定程度的不确定性，这样的预测是不可避免的，无论多么准确的是初始数据。在工作的洛伦茨可以看出，混沌行为的一个系统相对于初始条件介绍了该地区的动力系统理论。通常，动力系统被给出为事件空间上的变换。关于流形上的动力系统，人们提出了一个有趣的问题：“在所有的曲面超同态空间中，公理为A的超同态是C^1-稠密的吗？“我们的项目可以为这个重要问题提供答案。

项目成果

Taku Matsui: "Markov Semigroups which dcocribe the time evolution" J.Fun.Anal.,. 116. 179-198 (1993)

Taku Matsui：“记录时间演化的马尔可夫半群”J.Fun.Anal.,。

N.Aoki,J.Tomiyama: "Charactrizations of topological dynamical systems…" Ergod.Th.& Dynam.Sys.13. 1-5 (1993)

N.Aoki、J.Tomiyama：“拓扑动力系统的特征……”Ergod.Th.& Dynam.Sys.13 (1993)。

N.Aoki,J.Tomiyama: "Characterizations of topological dynamical systems…" Ergod.Th.& Dynami.Sys.13. 1-5 (1993)

N.Aoki、J.Tomiyama：“拓扑动力系统的特征……”Ergod.Th.& Dynami.Sys.13 (1993)。

Taku Matsui: "On conservation laws of the XY model" H.Araki(eds.),Quantum and Non-Commutative Analysis. 197-204 (1993)

Taku Matsui：“关于 XY 模型的守恒定律”H.Araki（编辑），量子和非交换分析。

Nobuo Aoki: "The set of axiom A diffeomorphisms with no cycles" Bol.Soc.Bras.Math.23. 21-65 (1992)

Nobuo Aoki：“没有循环的公理 A 微分同胚集”Bol.Soc.Bras.Math.23。