An attempt toward a solution to the C^r-stability conjecture (r【greater than or equal】2)

尝试解决C^r稳定性猜想(r【大于或等于】2)

基本信息

  • 批准号:
    15540197
  • 负责人:
  • 金额:
    $ 1.34万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
  • 财政年份:
    2003
  • 资助国家:
    日本
  • 起止时间:
    2003 至 2004
  • 项目状态:
    已结题

项目摘要

The dynamical systems theory originated from two notions of hyperbolicity and structural stability, and researches toward a solution to the stability conjecture played an important role in the developments of the theory. The conjecture asserts every structurally stable system is hyperbolic, and in 1987 it was proved by Mane for r=1. In the proof, so-called Franks lemma was essential. Since the lemma does not work for the C^r-topology (r【greater than or equal】2), the conjecture is still open when r【greater than or equal】2. The purpose of this research project is to prove the hyperbolicity under the shadowing-C^r-open condition (r【greater than or equal】2) fusing with Pesin theory, and by applying the techniques obtained in this process, we try to solve the C^r-stability conjecture for r 【greater than or equal】 2.In 2003, we restrict ourselves to 2-dimensional dynamical systems and concentrated to prove the hyperbolicity of the system under the shadowing-C^r-open condition. In 2004, we continuously proceeded the above strategy, but there were noting special for publication. However, for some partial results obtained in this research, we have found some handles to generalize them for higher dimensions. In our opinion, the achieve percentage of this project might be evaluated 50%.Before to show the hyperbolicity of the dynamical systems, it is necessary to prove the hyperbolicity of the periodic points. Under the shadowing-C^r-open condition (r【greater than or equal】2), the head investigator proved the hyperbolicity of the periodic points etc., and making use of the facts, he also proved the hyperbolicity for 2-dimensional dynamical systems by assuming additional conditions (as was stated it turned out that this result can be generalized).A base of this research project has been completed. Hereafter we would like to do my best to complete the project.
动力系统理论起源于双曲性和结构稳定性两个概念,而对稳定性猜想的求解在理论发展中起了重要作用。这个猜想断言每个结构稳定的系统都是双曲的,并且在1987年由马内证明了r=1。在证明中,所谓的弗兰克斯引理是必要的。由于引理不适用于C^r-拓扑(r[大于或等于]2),所以当r[大于或等于]2时,猜想仍然是开放的。本研究项目的目的是在阴影-C ^r-开条件下证明双曲性(r[大于或等于]2)与Pesin理论相融合,并应用在这一过程中得到的技巧,我们试图解决r [大于或等于] 2的C^r-稳定性猜想。我们把自己限制在2维动力系统,并集中于证明系统的双曲性下的shadowing-C^r-开条件。2004年,我们继续推进上述战略,但没有特别的出版物。然而,对于在本研究中得到的一些部分结果,我们已经找到了一些处理,以推广到更高的维度。在证明动力系统的双曲性之前,首先要证明周期点的双曲性。在阴影-C ^r-开条件(r[大于或等于]2)下,首席研究员证明了周期点等的双曲性,并利用这一事实,通过附加条件的假设,证明了二维动力系统的双曲性(如前所述,证明了这一结果是可以推广的),为该研究项目奠定了基础。今后我们将尽最大努力完成这项工程。

项目成果

期刊论文数量(21)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
$C^1$-stably positively expansive maps
$C^1$-稳定的正扩展地图
Sakai, Kazuhiro: "C^1-stably positively expansive maps"Bulletin of the Polish Academy of Sciences, Mathematics. (to appear). (2004)
Sakai,Kazuhiro:“C^1-稳定正扩张图”波兰科学院通报,数学。
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    0
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  • 通讯作者:
C^1-stably expansive maps
C^1-稳定扩展的地图
Sakai, Kazuhiro: "Various shadowing properties for positively expansive maps"Topology and its Applications. 131. 15-31 (2003)
Sakai,Kazuhiro:“正扩展地图的各种阴影属性”拓扑及其应用。
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  • 影响因子:
    0
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Sakai, Kazuhiro, S.Pilyugin, A.Rodionova: "Orbital and weak shadowing properties"Discrete and Continuous Dynamical Systems. 9. 287-308 (2003)
Sakai、Kazuhiro、S.Pilyugin、A.Rodionova:“轨道和弱阴影特性”离散和连续动力系统。
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  • 影响因子:
    0
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SAKAI Kazuhiro其他文献

SAKAI Kazuhiro的其他文献

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{{ truncateString('SAKAI Kazuhiro', 18)}}的其他基金

Integrability in gauge-gravity correspondence and gluon scattering amplitudes
规范重力对应和胶子散射振幅的可积性
  • 批准号:
    22740172
  • 财政年份:
    2010
  • 资助金额:
    $ 1.34万
  • 项目类别:
    Grant-in-Aid for Young Scientists (B)
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
  • 财政年份:
    2010
  • 资助金额:
    $ 1.34万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
ON THE CHARACTERIZATION OF CHAIN COMPONENTS BY MEANS OF THE SHADOWING PROPERTY
论用影子特性表征链元件
  • 批准号:
    19540209
  • 财政年份:
    2007
  • 资助金额:
    $ 1.34万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Developing participatory intervention toolkits and its monitoring systems for workplace risk reduction by health care workers in Asia
开发参与式干预工具包及其监测系统,以减少亚洲医护人员的工作场所风险
  • 批准号:
    19406018
  • 财政年份:
    2007
  • 资助金额:
    $ 1.34万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
A study on the characterization of C^r-diffeomorphisms possessing the shadowing property
具有遮蔽性质的C^r-微分同胚的表征研究
  • 批准号:
    17540187
  • 财政年份:
    2005
  • 资助金额:
    $ 1.34万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
The Effacts of Work-Family Balance and Health on Work Environment and Family Responsibility in Nursing with Shift Work.
轮班护理中工作与家庭平衡和健康对工作环境和家庭责任的影响。
  • 批准号:
    16510210
  • 财政年份:
    2004
  • 资助金额:
    $ 1.34万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
The Effects of Work-Family Balance and Health on Work Environment and Family Responsibility in Nursing with Shift Work.
轮班护理中工作与家庭平衡和健康对工作环境和家庭责任的影响。
  • 批准号:
    14594029
  • 财政年份:
    2002
  • 资助金额:
    $ 1.34万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Bifurcations of vector fields possessing the shadowing property
具有阴影特性的矢量场的分叉
  • 批准号:
    13640225
  • 财政年份:
    2001
  • 资助金额:
    $ 1.34万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Establishment of exposure risk assessment technique with continuous monitoring of personal environment.
建立持续监测个人环境的暴露风险评估技术。
  • 批准号:
    11470114
  • 财政年份:
    1999
  • 资助金额:
    $ 1.34万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Bifurcations of Dynamical Systems Satisfying the Pseudo-orbit Tracing Property
满足伪轨道追迹性质的动力系统的分岔
  • 批准号:
    11640217
  • 财政年份:
    1999
  • 资助金额:
    $ 1.34万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
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