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散逸的なランダム力学系に対する無限不変測度の構成と無限測度混合性への応用

耗散随机动力系统的无限不变测度的构造及其在无限测度混合特性中的应用

基本信息

批准号：
21K20330
负责人：
豊川永喜
金额：
$ 2万
依托单位：
Kitami Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Research Activity Start-up
财政年份：
2021
资助国家：
日本
起止时间：
2021-08-30 至 2024-03-31
项目状态：
已结题

项目摘要

昨年度に引き続き，散逸的な力学系から引き起こされるランダム力学系やマルコフ作用素に対する，絶対連続な不変測度の構成の研究を進めた．昨年度から続けていたBarrientos氏(Fluminense連邦大学)，中野氏(東海大学)，中村氏(北見工業大学)との国際共同研究では，独立同分布に従うランダム力学系に対して，有限個の絶対連続なエルゴード的不変確率測度(特に物理的測度)が存在し，特に不変測度の台が最大であるという条件を満たすための必要十分条件を与え，さらにマルコフ作用素に対して種々のconstrictivityという概念を導入し，かつ各々に対応するランダム力学系の具体例を与えることで，力学系の統計的性質に関する新たな分類を与えた．以上の結果をまとめた論文を現在投稿中である．この共同研究から派生して，不変測度が必ずしも確率測度でない場合，すなわち有限個の絶対連続なエルゴード的σ-有限不変測度が存在するための同値条件についても単独研究で導出し，現在論文準備中である．矢野氏(京都大学)，中野氏，中村氏との共同研究で得られた，区間上の2つの散逸的な変換を確率的に選択して与えられるランダム力学系に対する一般化逆正弦法則およびDarling--Kac則の結果に関しては，論文にまとめ，国際学術雑誌「Nonlinearily」に掲載された．昨年度から始めた井上氏(愛媛大学)との共同研究では，共通の中立不動点をと非常に散逸的に振る舞う枝を持つ区分的に凸な一次元ランダム力学系に対して，ルベーグ測度に絶対連続なエルゴード的σ-有限不変測度の存在及び不動点周りでの不変測度の評価を与え，結果をまとめた論文を現在投稿中である．

Last year, the Department of Mechanics was introduced to the Department of Mechanics, Nakamura, Nakamura There is an uncertainty test (the measure of special physics) for a limited number of customer-linked computers in the department of mechanical science of independent and uniformly distributed trunks, and there is a special measurement of the maximum load of the Taiwan company. it is necessary to apply ten percent of the necessary conditions, and the concepts of two kinds of constrictivity functions are introduced into the system. Each department of mechanics is required to provide specific examples and statistics of the Department of Mechanics, and the statistics of the Department of Mechanics are classified into categories and classes. as a result of the above results, the paper is now available in the submission. We will jointly study the derivative equipment, and it is necessary to ensure the accuracy of the test. The σ-finite measurement of a limited number of customer connections exists under the same conditions. The study of independence is now under preparation. Yano (Kyoto University), Nakano and Nakamura jointly studied the results of the study. The results of the general inverse sinusoidal method and the results of the general inverse sinusoidal method of the department of mechanical science of the department of mechanical science, department of mechanical science, department of mechanics, department of mechanical mechanics, department of mechanics, department of mechanical mechanics, department of mechanics, department of mechanical mechanics, department of mechanics, department of mechanical mechanics, department of physics, department of mechanics, department of It is common that the neutral point is very loose, and the vibration dance branch holds the distinction between the convex point and the mechanical system of the department of mechanics. in order to measure the existence of the σ-finite degree of measurement and the accuracy of the system, the results show that the data is now available in the submission.