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Ergodic Properties of Smooth Systems on Manifolds

流形上光滑系统的遍历性质

基本信息

批准号：
1956310
负责人：
Adam Kanigowski
金额：
$ 16.15万
依托单位：
University of Maryland, College Park
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-06-01 至 2023-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1956310&HistoricalAwards=false
关键词：
Ergodic Properties Smooth Systems Manifolds

项目摘要

This research project concerns the chaotic properties of smooth dynamical systems. Smooth dynamical systems may exhibit chaotic behavior, this is where the future evolution of the systems is strongly independent of its present state and the evolution behaves like a sequence of independent coin tosses. The principal investigator plans to study such chaotic behavior for a wide class of natural dynamical systems. The developed methods will result in progress in the understanding of fundamental dynamical phenomena, with possible applications to other mathematical fields such as geometry and number theory, and also to the natural sciences. The principal investigator also plans to be involved in synergistic activities including organizing conferences and working with graduate students and postdocs.Chaotic properties of (uniformly) hyperbolic systems are by now well understood. Much less is known for partially hyperbolic systems, especially those with non-trivial (fast) growth on the center space. The principal investigator plans to create a general framework for studying K and Bernoulli properties for partially hyperbolic systems, and also plans to study mixing and spectral properties of parabolic systems, trying to further develop a general theory for systems of polynomial orbit growth.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

本研究计画主要探讨光滑动力系统的混沌特性。光滑动力系统可能表现出混沌行为，这是系统的未来演化与其当前状态强烈无关，并且演化表现得像一系列独立的硬币投掷。首席研究员计划研究一大类自然动力系统的混沌行为。所开发的方法将导致进步的基本动力学现象的理解，与可能的应用到其他数学领域，如几何和数论，以及自然科学。首席研究员还计划参与协同活动，包括组织会议，并与研究生和博士后合作。（一致）双曲系统的混沌特性现在已经很好地理解。对于部分双曲系统，特别是那些在中心空间上具有非平凡（快速）增长的系统，所知要少得多。首席研究员计划为研究部分双曲系统的K和Bernoulli性质创建一个通用框架，并计划研究抛物系统的混合和光谱性质，试图进一步发展多项式轨道增长系统的一般理论。该奖项反映了美国国家科学基金会的法定使命，并被认为是值得通过利用基金会的智力价值和更广泛的影响审查进行评估来支持的的搜索.