間欠カオス力学系のエルゴード理論的解析

间歇混沌动力系统的遍历分析

• 批准号: 08740148
• 负责人: 井上 友喜
• 金额: $ 0.64万
• 依托单位: Ehime University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Encouragement of Young Scientists (A)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08740148/
• 关键词: エルゴード理論; 離散力学系; 間欠カオス; σ一有限不変測度

本研究開始前,間欠カオスを生じるようなある特別なクラスの一次元写像の力学系におけるエルゴード理論的に意味のあるある種の極限について研究し,その極限の存在および極限値に関する結果を得ていた.そこで,本研究は,・最近成功した特別なクラスの一次元写像に対する結果を興味深い例を含む一般的な一次元写像に対するものに拡張することと,・エルゴード理論的に意味のある時間平均の極限値が定まらずに振動するような条件を得ること,間欠カオスがみられる多次元の力学系に対しても,同様の極限について予備的な考察をすることを目的として実施した.性能がよく使い勝手がよいコンピュータを購入して,数値実験・シミュレーションによって,ある程度の状況を把握し,予測をたて,また,この研究において重要な確率論,力学系に関連した図書を購入して活用し,さらに,研究の進展にあわせて,確率論や力学系の専門家と直接会って,この研究の進展状況を説明し,意見交換を行ったり,専門的知識・資料の提供を受けたりして,それらを参考にして研究を行った.その結果,私が最近成功した特別なクラスの一次元写像に対する結果を,興味深い例を含む一般的な一次元写像に対するものに拡張することができた.また,時間平均の極限値が定まらずに振動するような写像のクラスを見いだすことができた.また,間欠カオスを生じるような多次元の力学系に対しても今後の研究のための予備的考察を行うことができた.なお,この研究の成果を確率論関係の国際会議等において発表した.

Before the beginning of this study, the students of the Department of Mechanics wrote the first step of this study, which means that there is a limit for the study of mathematics in the Department of Mechanics. the results show that the results are satisfactory. In this study, recently, we have successfully verified one-dimensional writing for a special purpose, such as the results of the experiment, the results of the test, the results of the test, and the general example of the first-order write, which is similar to that of the general one, which means that the average time limit of the simulation theory means that the average time limit is good. The Department of Mechanics is in the same position as the department of mechanics, which is the same as that of the Department of Mechanics. In terms of performance, you can learn how to improve your performance. You need to know how much you want to know about how much you want to know, and how to make sure that you have a good understanding of how much you want to know, and how to make sure that you are aware of the importance of the study, the department of mechanics, the department of mechanics. The progress of the research is clear, the exchange of opinions is discussed, the knowledge data of the department is provided, and the information is referred to the research bank. The results show that recently, we have successfully verified the results of one-dimensional writing, which is similar to the results of the experiment, and the case of deep taste is similar to that of the general one. The average time limit is to determine the frequency of the vibration and write the image of the car. In the future, the Department of Mechanics will study the investigation of the equipment in the future. The results of the research and the confirmation rate of the results of the research are related to the international conferences.

项目成果

INOUE,TOMOKI: "Ratio ergodic theorems for maps with indifferent fixed points" Ergodic Theory and Dynamical Systems. 17. 1-18 (1997)

INOUE,TOMOKI：“具有无关不动点的地图的比率遍历定理”遍历理论和动力系统。