ON THE CHARACTERIZATION OF HOMOCLINIC CLASSES BY MEANS OF THE SHADOWING PROPERTY

论用阴影性质表征同宿类

• 批准号: 22540218
• 负责人: SAKAI Kazuhiro
• 金额: $ 1.91万
• 依托单位: Utsunomiya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540218/
• 关键词: 力学系; 力学系理論; 擬軌道尾行性; ホモクリニッククラス; 双曲性; 占有的分割

Since Anosov and Bowen's works, the notion of the pseudo-orbit shadowing property very often appears in the several branches of the theory of dynamical systems, and usually plays an important role in the investigation. The latest developments of the shadowingtheory of dynamical systems are very remarkable; in fact, the shadowing theory is not only a base of numerical study of dynamical systems but also gives rise to lots of important consequences in qualitative theory of dynamical systems. The purpose of this research project is to characterize the dynamical systems or subsystems possessing the shadowing property from view point of the differential geometric theory of dynamical systems.

由于Anosov和Bowen的作品，伪轨遮蔽特性的概念经常出现在动态系统理论的几个分支中，并且通常在研究中起重要作用。动态系统阴影理论的最新发展非常出色。实际上，阴影理论不仅是动态系统的数值研究的基础，而且在动态系统的定性理论中产生了许多重要的后果。该研究项目的目的是表征从动力学系统的差异几何理论的角度具有阴影属性的动力系统或子系统。

项目成果

Positively expansive differentiable maps

正可微分映射

• 发表时间: 2010
• 期刊: Acta Mathematica Sinica, English Series
• 作者: K.Sakai

Regular maps satisfying the specification property

满足规格属性的正则地图

• DOI: 10.3934/dcds.2013.33.2991
• 发表时间: 2013
• 期刊: Discrete and Contin. Dynam. Syst.
• 作者: K. Moriyasu;K. Sakai and K. Yamamoto
• 通讯作者: K. Sakai and K. Yamamoto

Measure-expansive diffeomorphisms

测度扩张微分同胚

• DOI: 10.1016/j.jmaa.2014.01.023
• 发表时间: 2014
• 期刊: J. Math. Anal. Appl
• 作者: K. Sakai;N. Sumi;K. Yamamoto
• 通讯作者: K. Yamamoto

C1-stably weakly shadowing homoclinic classes, Various Aspects of Dynamical Systems, ICM 2010 Satellite Conference

C1-稳定弱阴影同宿类，动力系统的各个方面，ICM 2010 卫星会议

• 发表时间: 2010
• 作者: Satoshi Tsujimoto;Luc Vinet and Alexei Zhedanov;K.Sakai;K. Sakai
• 通讯作者: K. Sakai

C^1-stably weakly shadowing homoclinic classes admit dominated splittings

C^1-稳定的弱阴影同宿类承认主导分裂

• 发表时间: 2010
• 期刊: Discrete and Continuous Dynamical Systems
• 影响因子: 1.1
• 作者: S.Gan;K.Sakai;L.Wen
• 通讯作者: L.Wen