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
- 来源:
- 关键词:
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推动该领域发展的一个激励问题。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数次逆转。近可积系统是稳定的还是不稳定的?答案可能是两者兼而有之:在测量理论意义上,大多数轨道是稳定的(KAM定理);从拓扑意义上来说,大多数系统可能都是不稳定的。我们研究的主要目标是了解不稳定性。由于稳定与不稳定并存,这样的问题往往很难解决。我们特别对阿诺德在1963年提出的猜想感兴趣,即对于一个典型的近可积系统,不稳定性和KAM现象并存。我和我的合著者开发了非常适合研究这些问题的新方法。我建议研究以下课题: 1.发现比阿诺德预测的更不稳定的轨道,这些轨道在某种意义上表现出混乱。 2. 研究阿诺德关于更高维度的问题。 3、继续发展相关理论,阐明稳定与不稳定共存的奥秘。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Zhang, Ke其他文献
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
Digital Twin Networks: A Survey
- DOI:
10.1109/jiot.2021.3079510 - 发表时间:
2021-09-15 - 期刊:
- 影响因子:10.6
- 作者:
Wu, Yiwen;Zhang, Ke;Zhang, Yan - 通讯作者:
Zhang, Yan
Influence of TiN-nanolayered insertions on microstructure and mechanical properties of TiSiN nanocomposite film
TiN纳米层插入对TiSiN纳米复合薄膜微观结构和力学性能的影响
- DOI:
10.1007/s10853-014-8107-5 - 发表时间:
2014-02 - 期刊:
- 影响因子:4.5
- 作者:
Li, Wei;Liu, Ping;Zhu, Xiaodong;Zhang, Ke;Ma, Fengcang;Liu, Xinkuan;Chen, Xiaohong;He, Daihua - 通讯作者:
He, Daihua
19F- and fluorescently labeled micelles as nanoscopic assemblies for chemotherapeutic delivery.
- DOI:
10.1021/bc800396h - 发表时间:
2008-12 - 期刊:
- 影响因子:4.7
- 作者:
Du, Wenjun;Xu, Zhiqiang;Nystroem, Andreas M.;Zhang, Ke;Leonard, Jeffrey R.;Wooley, Karen L. - 通讯作者:
Wooley, Karen L.
Unique post-functionalization method for ROMP polymers based on Triazolinedione Alder-ene chemistry
基于三唑啉二酮 Alder-ene 化学的 ROMP 聚合物独特的后官能化方法
- DOI:
10.1016/j.polymer.2015.07.050 - 发表时间:
2015-09 - 期刊:
- 影响因子:4.6
- 作者:
Zhao, Yuming;Chen, Jiqiang;Zhu, Wen;Zhang, Ke - 通讯作者:
Zhang, Ke
Zhang, Ke的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ 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)
Study of the energy level statistics for classically integrable and nearly integrable quantum systems
经典可积和近可积量子系统的能级统计研究
- 批准号:
18740241 - 财政年份:2006
- 资助金额:
$ 1.75万 - 项目类别:
Grant-in-Aid for Young Scientists (B)