Instabilities in nearly integrable Hamiltonian systems

近可积哈密顿系统的不稳定性

基本信息

  • 批准号:
    436169-2013
  • 负责人:
  • 金额:
    $ 1.75万
  • 依托单位:
  • 依托单位国家:
    加拿大
  • 项目类别:
    Discovery Grants Program - Individual
  • 财政年份:
    2017
  • 资助国家:
    加拿大
  • 起止时间:
    2017-01-01 至 2018-12-31
  • 项目状态:
    已结题

项目摘要

A good example of nearly integrable systems is the solar system. Indeed, the stability of the solar system has been a motivating question that drives the field. Since Poincaré's proof that the planar three body question is not integrable, the answer to the stability question has gone through several reversals. Are nearly integrable systems stable or unstable? The answer is probably both: in the measure theoretical sense, most orbits are stable (KAM Theorem); in the topological sense, most systems are probably unstable. The main goal of our research is to understand the instabilities. Due to the coexistence of stability and instability, such question are often very difficult. We are, in particular, interested in the conjecture of Arnold in 1963, that for a typical nearly integrable system, there is coexistence of instability and KAM phenomenon. My coauthors and I have developed new approaches well suited to study these problems. I propose research in the following topics:1. Find even more unstable orbits than Arnold predicted, these orbits exhibits chaos in a certain sense. 2. Investigate Arnold's question for higher dimensions. 3. Continue to develop the related theories that help clarify the mysteries behind the coexistence of stability and instability.
近似可积系统的一个很好的例子是太阳系。事实上,太阳系的稳定性一直是驱动该领域的一个激励性问题。自从庞加莱证明平面三体问题不可积以来,稳定性问题的答案经历了几次逆转。近似可积系统是稳定的还是不稳定的?答案可能是两者都有:在测度论意义上,大多数轨道是稳定的(KAM定理); 2在拓扑意义上,大多数系统可能是不稳定的。我们研究的主要目的是了解不稳定性。由于稳定与不稳定并存,这样的问题往往非常困难。我们特别感兴趣的是Arnold在1963年提出的一个猜想,即对于一个典型的近可积系统,不稳定性和KAM现象是共存的。我和我的合著者已经开发出了非常适合研究这些问题的新方法。我建议在以下几个方面进行研究:1。发现比Arnold预测的更不稳定的轨道,这些轨道在一定意义上表现出混沌。2.研究阿诺德的高维问题。3.继续发展相关理论,帮助澄清稳定与不稳定共存背后的奥秘。

项目成果

期刊论文数量(0)
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会议论文数量(0)
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Zhang, Ke其他文献

Well-defined cationic shell crosslinked nanoparticles for efficient delivery of DNA or peptide nucleic acids.
Cognitive improvement effect of nervonic acid and essential fatty acids on rats ingesting Acer truncatum Bunge seed oil revealed by lipidomics approach
  • DOI:
    10.1039/d1fo03671h
  • 发表时间:
    2022-01-21
  • 期刊:
  • 影响因子:
    6.1
  • 作者:
    Song, Wangting;Zhang, Ke;Chen, Xianyang
  • 通讯作者:
    Chen, Xianyang
Binding proteins of destruxin A from Metarhizium against insect cell.
  • DOI:
    10.1186/s12866-023-02843-8
  • 发表时间:
    2023-04-04
  • 期刊:
  • 影响因子:
    4.2
  • 作者:
    Wang, Jingjing;Weng, Qunfang;Zhang, Ke;Hu, Qiongbo
  • 通讯作者:
    Hu, Qiongbo
Modular construction of macrocycle-based topological polymers via high-efficient thiol chemistry
通过高效硫醇化学模块化构建大环拓扑聚合物
  • DOI:
    10.1039/c5py00174a
  • 发表时间:
    2015-03
  • 期刊:
  • 影响因子:
    4.6
  • 作者:
    Zhou, Nianchen;Zhang, Ke;Zhang, Zhengbiao;Zhu, Xiulin
  • 通讯作者:
    Zhu, Xiulin
Poly(ADP-ribose) promotes toxicity of C9ORF72 arginine-rich dipeptide repeat proteins.
  • DOI:
    10.1126/scitranslmed.abq3215
  • 发表时间:
    2022-09-14
  • 期刊:
  • 影响因子:
    17.1
  • 作者:
    Gao, Junli;Mewborne, Quinlan T.;Girdhar, Amandeep;Sheth, Udit;Coyne, Alyssa N.;Punathil, Ritika;Kang, Bong Gu;Dasovich, Morgan;Veire, Austin;Hernandez, Mariely DeJesus;Liu, Shuaichen;Shi, Zheng;Dafinca, Ruxandra;Fouquerel, Elise;Talbot, Kevin;Kam, Tae-In;Zhang, Yong-Jie;Dickson, Dennis;Petrucelli, Leonard;Van Blitterswijk, Marka;Guo, Lin;Dawson, Ted M.;Dawson, Valina L.;Leung, Anthony K. L.;Lloyd, Thomas E.;Gendron, Tania F.;Rothstein, Jeffrey D.;Zhang, Ke
  • 通讯作者:
    Zhang, Ke

Zhang, Ke的其他文献

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{{ truncateString('Zhang, Ke', 18)}}的其他基金

Instabilities in Hamiltonian systems
哈密​​顿系统的不稳定性
  • 批准号:
    RGPIN-2019-07057
  • 财政年份:
    2022
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Instabilities in Hamiltonian systems
哈密​​顿系统的不稳定性
  • 批准号:
    RGPIN-2019-07057
  • 财政年份:
    2021
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Instabilities in Hamiltonian systems
哈密​​顿系统的不稳定性
  • 批准号:
    RGPIN-2019-07057
  • 财政年份:
    2020
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Instabilities in Hamiltonian systems
哈密​​顿系统的不稳定性
  • 批准号:
    RGPIN-2019-07057
  • 财政年份:
    2019
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Instabilities in nearly integrable Hamiltonian systems
近可积哈密顿系统的不稳定性
  • 批准号:
    436169-2013
  • 财政年份:
    2018
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Reinforcement learning approach to large scale dynamic pricing
大规模动态定价的强化学习方法
  • 批准号:
    510818-2017
  • 财政年份:
    2017
  • 资助金额:
    $ 1.75万
  • 项目类别:
    University Undergraduate Student Research Awards
Instabilities in nearly integrable Hamiltonian systems
近可积哈密顿系统的不稳定性
  • 批准号:
    436169-2013
  • 财政年份:
    2016
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Instabilities in nearly integrable Hamiltonian systems
近可积哈密顿系统的不稳定性
  • 批准号:
    436169-2013
  • 财政年份:
    2015
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Instabilities in nearly integrable Hamiltonian systems
近可积哈密顿系统的不稳定性
  • 批准号:
    436169-2013
  • 财政年份:
    2014
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Instabilities in nearly integrable Hamiltonian systems
近可积哈密顿系统的不稳定性
  • 批准号:
    436169-2013
  • 财政年份:
    2013
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual

相似海外基金

Singular limits in nearly integrable quantum systems and complex dynamical systems
近可积量子系统和复杂动力系统中的奇异极限
  • 批准号:
    22H01146
  • 财政年份:
    2022
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Impurities and disorder in nearly integrable models
近可积模型中的杂质和无序
  • 批准号:
    421428100
  • 财政年份:
    2019
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Research Units
Instabilities in nearly integrable Hamiltonian systems
近可积哈密顿系统的不稳定性
  • 批准号:
    436169-2013
  • 财政年份:
    2018
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Singular nature in nearly integrable Hamiltonian systems and breakdown of classical-quantum correspondence
近可积哈密顿系统的奇异性和经典量子对应的分解
  • 批准号:
    17K05583
  • 财政年份:
    2017
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Instabilities in nearly integrable Hamiltonian systems
近可积哈密顿系统的不稳定性
  • 批准号:
    436169-2013
  • 财政年份:
    2016
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Instabilities in nearly integrable Hamiltonian systems
近可积哈密顿系统的不稳定性
  • 批准号:
    436169-2013
  • 财政年份:
    2015
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Instabilities in nearly integrable Hamiltonian systems
近可积哈密顿系统的不稳定性
  • 批准号:
    436169-2013
  • 财政年份:
    2014
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Instabilities in nearly integrable Hamiltonian systems
近可积哈密顿系统的不稳定性
  • 批准号:
    436169-2013
  • 财政年份:
    2013
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Discovery Grants Program - Individual
Multi ergodicity in nearly integrable Hamiltonian systems and large deviation properties of infinite ergodic systems
近可积哈密顿系统的多重遍历性和无限遍历系统的大偏差性质
  • 批准号:
    21540399
  • 财政年份:
    2009
  • 资助金额:
    $ 1.75万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
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经典可积和近可积量子系统的能级统计研究
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  • 财政年份:
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  • 项目类别:
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