RUI: Cocycles and rigidity for hyperbolic systems and actions
RUI:双曲系统和作用的余循环和刚度
基本信息
- 批准号:1101150
- 负责人:
- 金额:$ 8.92万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2011
- 资助国家:美国
- 起止时间:2011-06-01 至 2014-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The main objects of the proposed research are smooth dynamical systems such as diffeomorphisms and flows, as well as smooth actions of higher rank abelian groups. The main goal of the project is to study various rigidity properties for hyperbolic, partially hyperbolic, and non-uniformly hyperbolic systems and actions. Higher rank actions exhibit remarkable properties including rigidity of invariant measures and smooth rigidity. In rank one case, rigidity occurs for some non-typical systems, such as those with high smoothness of invariant foliations or strong pinching. An important role in both areas is played by cocycles. Investigating cohomology of non-commutative cocycles over hyperbolic systems is a major part of the proposed research.The field of Dynamical Systems studies evolution of mechanical, physical, and mathematical systems over time. It provides applications to other areas of mathematics as well as to many natural sciences such as physics, mechanics, computer science, and biology. This field originated from differential equations and celestial mechanics. It uses mathematical tools from analysis and topology to study qualitative behavior of systems "in the long run". A major part of the project is the study of more complex systems consisting of several individual ones that commute with each other. Such complex systems appear naturally in algebra, geometry, and physics. The PI works for the main regional university which is primarily undergraduate and educates most of the local school teachers.-----------------------------------------------------
本文的主要研究对象是光滑动力系统,如微分同胚和流,以及高阶阿贝尔群的光滑作用。该项目的主要目标是研究双曲型、部分双曲型和非一致双曲型系统和作用的各种刚性性质。高阶作用具有不变测度的刚性和光滑刚性等显著性质。在第一种情况下,一些非典型系统会出现刚性,例如具有高不变叶光滑性或强收缩的系统。共循环在这两个领域都发挥着重要作用。研究双曲系统上非对易上循环的上同调是所提出的研究的主要部分。动力系统领域研究力学、物理和数学系统随时间的演化。它提供了数学的其他领域以及许多自然科学的应用,如物理、力学、计算机科学和生物学。这个领域起源于微分方程式和天体力学。它使用分析和拓扑学中的数学工具来研究“长期”系统的定性行为。该项目的一个主要部分是研究更复杂的系统,这些系统由几个相互通勤的独立系统组成。这样的复杂系统在代数、几何和物理中很自然地出现。PI为主要的地区性大学工作,该大学主要是本科生,并为当地大部分学校提供teachers.-----------------------------------------------------教育
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)
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Boris Kalinin其他文献
Boris Kalinin的其他文献
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{{ truncateString('Boris Kalinin', 18)}}的其他基金
Measure rigidity and smooth rigidity of abelian actions
测量阿贝尔动作的刚度和平滑刚度
- 批准号:
0701292 - 财政年份:2007
- 资助金额:
$ 8.92万 - 项目类别:
Standard Grant
Rigidity Phenomena for Higher Rank Abelian Actions
高阶阿贝尔动作的刚性现象
- 批准号:
0411769 - 财政年份:2003
- 资助金额:
$ 8.92万 - 项目类别:
Standard Grant
Rigidity Phenomena for Higher Rank Abelian Actions
高阶阿贝尔动作的刚性现象
- 批准号:
0140513 - 财政年份:2002
- 资助金额:
$ 8.92万 - 项目类别:
Standard Grant
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Cocycles的动力学及其在线性算子谱理论中的应用
- 批准号:10871090
- 批准年份:2008
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Geometric cocycles, differential K-theory, and non-abelian gerbes
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