Study of foliations and discrete group actions

叶状结构和离散群体行为的研究

• 批准号: 20540096
• 负责人: MATSUMOTO Shigenori
• 金额: $ 2.16万
• 依托单位: Nihon University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540096/
• 关键词: 葉層構造; 群作用; 円周上の微分可能同窓写像; 回転数; Liouville 数; 離散群作用; 平面写像; 連続体; prime end; Liouville数; ヘルダー連続; 絶対連続; 離散群; 多様体; エルゴード性; 極小集合; 基本領域; 不変測度; パラメータ剛性; Diophantus条件; 調和測度; 特異測度; 力学系; 流れ; リー群; 剛性

Assume that a homeomorphism of the plane admits a compact minimal set which is connected and not a point. We showed that there are exactly two invariant connected components of the complement. We also showed that the rotation number is uniquely determined. Given a foliation on a compact manifold and a leafwise Riemannian metric, there is defined a harmonic measure of the manifold. In case the metric is hyperbolic and the harmonic measure is ergodic, we showed that there is a dichotomy of the measures. Among flows along the Reeb foliation of the plane, there is one which is called standard. We characterized it by its dynamical property.

设平面的同胚存在一个连通的非点的紧极小集。我们证明了补的连通分支只有两个不变。我们还证明了旋转数是唯一确定的。给定紧致流形上的一个叶状结构和一个叶式黎曼度量，定义了该流形的一个调和测度。在度量是双曲的且调和测度是遍历的情况下，我们证明了测度的二分法。在沿着该平面的里布叶理的流中，有一种流被称为标准流。我们用它的动力学性质来描述它。

项目成果

A characterizaton ofthe standard Reeb flow

标准力波流的表征

• 发表时间: 2013
• 期刊: Hokkaido Math.Journal
• 作者: S. Matsumoto

Derivatives of rotation numbers of one parameter families of circle diffeomorphisms

圆微分同胚一参数族旋转数的导数

• 发表时间: 2012
• 期刊: Kodai Mathematical Journal
• 影响因子: 0.6
• 作者: S. Matsumoto;S. Matsumoto
• 通讯作者: S. Matsumoto

The unique ergodicity of equicontinuous laminations

等连续叠层的独特遍历性

• 发表时间: 2010
• 期刊: Hokkaido Journal of Mathematics
• 作者: 松元重則;中山裕道;松元重則;S. Matsumoto
• 通讯作者: S. Matsumoto

Normally contracting Lie group actions

通常收缩李群作用

• DOI: 10.1016/j.topol.2011.12.012
• 发表时间: 2012
• 期刊: Topology Appl
• 作者: Inaba;Takashi; Matsumoto;Shigenori; Mitsumatsu;Yoshihiko
• 通讯作者: Yoshihiko

Minimal C^1 diffeomorphisms of the circle which admit measurable fundamental domains

允许可测量基本域的圆的最小 C^1 微分同胚

• DOI: 10.1090/s0002-9939-2013-11472-3
• 发表时间: 2013
• 期刊: Proceedings of the American Mathematical Society
• 影响因子: 1
• 作者: Matsui;T;森本佳世子;Bambang Retnoaji;Tatsuro Matta;別所康全;別所 康全;Natsui Takaaki;森本佳世子;Bambang Retnoaji;Tatsuro Matta;Hiroki KODAMA and Shigenori MATSUMOTO
• 通讯作者: Hiroki KODAMA and Shigenori MATSUMOTO