On rotation sets for angular velocity

关于角速度的旋转集

• 批准号: 19540090
• 负责人: NAKAYAMA Hiromichi
• 金额: $ 2.91万
• 依托单位: Aoyama Gakuin University (2008-2009)Hiroshima University (2007)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540090/
• 关键词: 微分トポロジー; 力学系

The purpose of this study is to find periodic orbits by examining the twist of the tangent vectors along the orbits. I showed the existence of periodic orbits from the velocity and the infinitesimal twist, and also classified connected minimal sets from the topological points of view. Furthermore I characterized the variation of angles along the orbits in minimal sets. As a main result, I proved the following theorem (a joint work with Shigenori Matsumoto) ; "Let f be an orientation preserving homeomorphism of the sphere which has a nontrivial continuum as a minimal set. Then there are exactly two invariant domains in the complement of the minimal set and all the other domains are wandering."

这项研究的目的是通过检查沿轨道的切向量的扭曲来找到周期性轨道。我从速度和无穷小扭曲的角度证明了周期轨道的存在性，并从拓扑的角度对连通最小集进行了分类。此外，我还描述了最小集合中沿轨道的角度变化。作为主要结果，我证明了以下定理（与 Shigenori Matsumoto 合作）； “设 f 是保持球体同态的方向，它具有作为最小集的非平凡连续体。那么在最小集的补集中恰好有两个不变域，并且所有其他域都是徘徊的。”

项目成果

Modelling minimal foliated spaces with positive entropy

具有正熵的最小叶状空间建模

• 发表时间: 2007
• 作者: A. Bi's

Infinitesimal behavior of 2-dimensional dynamical systems

二维动力系统的无穷小行为

• 发表时间: 2007
• 作者: H. Nakayama

余次元2例外極小集合を持つ力学系について

具有共维二例外最小集的动力系统

• 发表时间: 2007
• 作者: 中山裕道

A lower estimat of the movement for twisted toral diffeomorphisms.

对扭曲托微分同胚运动的较低估计。

• 发表时间: 2008
• 作者: H. Nakayama

Fiberwise divergent orbits of projective flows with exactly two minimal sets

具有恰好两个最小集的投影流的纤维发散轨道

• 发表时间: 2007
• 作者: H. Nakayama