Research on ergodic theory and its applications

遍历理论及其应用研究

• 批准号: 06452017
• 负责人: ITO Yuji
• 金额: $ 4.22万
• 依托单位: Keio 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: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06452017/
• 关键词: type II^* & III transformations; Radon-Nikodym cocycles; exhaustive weakly wandering sequences; direct sum decompostion of 2; multiple recurrence; Kakutani-Parry index; cutting and stacking method; complexity of sequences; II_∞型及びIII型エルゴード変換; ラドン

In this project, researches concerning diversified areas connected with ergodic theory were carried out by a number of mathematicians working in the areas of ergodic theory, probability theory, functional analysis, analytic number theory, combinatorics and differential geometry, and many significant results were obtained.1. In ergodic theory proper, properties of ergodic transformations which are characteristic for transformations having no finite invariant measures (so-called typ II_* and type III transformations) were investigated in depth. In particular, asymptotic behavior of the Radon-Nikodym cocycles and properties of exhaustive weakly wandering sequences and their relation to the direct sum decomposition of the integers Z were studied and a number of interesting results were obtained. Furthermore, multiple recurrence properties of type II_* transformations were studied and their relation with Kakutani-Parry index was established.2. Concerning the interrelation between ergodic theory and othe areas, complexity of th esymbolic sequences associated with 3-dimensional billiard was determined, and sharp L^*-norm estimates for eigen functions for Laplacian on hyperbolic 3 manifolds were obtained.

在该项目中，关于与奇特理论相关的多元化领域的研究是由许多在厄基德理论，概率理论，功能分析，分析数理论，组合学和差异几何学领域工作的数学家进行的，并获得了许多重要的结果。1。在正常的理论中，对没有有限不变度的转换（所谓的典型ii_*和III型转换）的转换特征的特性进行了深入研究。特别是，研究了ra尼克近去共生的渐近行为和详尽的弱徘徊序列的特性及其与整数z的直接和总和分解的关系，并获得了许多有趣的结果。此外，研究了II_*类型的多个复发特性，并建立了与Kakutani-Parry指数的关系。2。关于沿着厄尔及性理论与奥特区域之间的相互关系，确定了与三维台球相关的埃甘贝序序列的复杂性，并获得了laplacian在双曲线3歧管上的特征函数的尖锐的l^* - 规范估计值。

项目成果

Enomoto,H.: "Graph decompositions without isolated vertices" Jour.of Combinatorial Theory. 63. 111-124 (1995)

Enomoto,H.：“没有孤立顶点的图分解”组合理论杂志。

Enomoto,H.,van den Heuvel Kaneko,A.& Saito.A.: "Relative length of long paths and cycles in graphs with large degree sums" Journal of Graph Theory. (to appear in).

Enomoto，H.，van den Heuvel Kaneko，A.

Shinya Koyama: "L^∞-norms of eigenfunctions for hyperbolic three manifolds" Duke Math. Journal. 77. 799-817 (1995)

Shinya Koyama：“双曲三流形的特征函数的 L^∞-范数”杜克数学杂志 77. 799-817 (1995)。

Maejima,M.: "Operator-stable processes and operator fractional stable motions" Probability and Mathematical Statistics. (to appear in).

Maejima,M.：“算子稳定过程和算子分数稳定运动”概率与数理统计。

Yuji Ito & M.Yoshida: "Cocycles for non-singular transformtions" Commentarii Math.Univ.St.Pauli. 44. 93-103 (1995)

伊藤雄二