Dynamical Systems: Theory and Applications

动力系统:理论与应用

基本信息

  • 批准号:
    0600974
  • 负责人:
  • 金额:
    $ 57.5万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2006
  • 资助国家:
    美国
  • 起止时间:
    2006-06-01 至 2012-05-31
  • 项目状态:
    已结题

项目摘要

Research topics within the theory of dynamical systems and on its applications are proposed. Four projects are described. The first proposes to leverage techniques developed for low dimensional systems to analyze (infinite dimensional) systems defined by evolutionary partial differential equations. Expected results include methods for detecting strange attractors in physical and mechanical systems. The second project is about networks of dynamical systems. It seeks to systematically relate the aggregate behaviors of such systems to those of their individual components and to the coupling. The third topic lies in the interface between dynamical systems and nonequilibrium statistical physics. One of the objectives here is to shed light on the notion of local equilibrium for systems with deterministic microscopic dynamics. The fourth and final topic is about large deviations, an important statistical property for dynamical systems. A scheme expected to resolve the issue for a large class of nonuniformly hyperbolic systems is proposed.This proposal addresses several topics at the frontier of research in dynamical systems, a branch of modern mathematics concerned with time evolutions of natural processes. Its main focus is the analysis of systems with high complexity, due either to multiple degrees of freedom or to chaos within the system. It is systems of this kind that are most often encountered in applications. The proposed methods of investigation include geometric analysis, probabilistic techniques and numerical simulations. A larger aim of the proposed work is to integrate dynamical systems ideas into other core areas of mathematics such as partial differential equations, and to build connections with other scientific disciplines such as statistical physics and the biological sciences. The resulting cross-fertilization is expected to be beneficial to all. In terms of educational value, the proposed research will provide ample training for emerging mathematicians, as it will involve directly the postdoctoral associates and Ph.D. students of the Principle Investigator.
提出了动力系统理论及其应用的研究课题。描述了四个项目。第一个建议利用低维系统开发的技术来分析(无限维)系统定义的演化偏微分方程。预期的结果包括在物理和机械系统中检测奇怪吸引子的方法。第二个项目是关于动力系统的网络。它试图系统地将这些系统的总体行为与它们的单个组件的行为以及耦合联系起来。第三个主题是动力学系统和非平衡统计物理之间的接口。这里的目标之一是阐明确定性微观动力学系统的局部平衡的概念。第四个也是最后一个主题是关于大偏差,这是动力系统的一个重要统计特性。本文提出了一个解决一类非一致双曲系统的方案,这一方案涉及到动力系统研究的几个前沿课题,动力系统是现代数学的一个分支,主要研究自然过程的时间演化。它的主要重点是分析具有高复杂性的系统,由于多个自由度或系统内的混沌。在应用中最经常遇到的就是这种系统。建议的调查方法包括几何分析,概率技术和数值模拟。拟议工作的一个更大的目标是将动力系统的思想整合到数学的其他核心领域,如偏微分方程,并与其他科学学科建立联系,如统计物理学和生物科学。预期由此产生的相互促进将对所有人都有利。就教育价值而言,拟议的研究将为新兴数学家提供充足的培训,因为它将直接涉及博士后和博士主要研究者的学生。

项目成果

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Lai-Sang Young其他文献

Extended Systems with Deterministic Local Dynamics and Random Jumps

Lai-Sang Young的其他文献

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{{ truncateString('Lai-Sang Young', 18)}}的其他基金

Dynamical Systems with a View towards Applications
着眼于应用的动力系统
  • 批准号:
    2350184
  • 财政年份:
    2024
  • 资助金额:
    $ 57.5万
  • 项目类别:
    Continuing Grant
Dynamical Systems: Connecting Theory to Applications
动力系统:理论与应用的结合
  • 批准号:
    1901009
  • 财政年份:
    2019
  • 资助金额:
    $ 57.5万
  • 项目类别:
    Continuing Grant
Frontiers in Dynamical Systems
动力系统前沿
  • 批准号:
    1363161
  • 财政年份:
    2014
  • 资助金额:
    $ 57.5万
  • 项目类别:
    Continuing Grant
Dynamical Systems: from Theory to Applications
动力系统:从理论到应用
  • 批准号:
    1101594
  • 财政年份:
    2011
  • 资助金额:
    $ 57.5万
  • 项目类别:
    Continuing Grant
Dynamical Systems
动力系统
  • 批准号:
    0100538
  • 财政年份:
    2001
  • 资助金额:
    $ 57.5万
  • 项目类别:
    Continuing Grant
Some Studies On Non-Uniformly Hyperbolic Attractors and the N-Body Problem
非均匀双曲吸引子与N体问题的一些研究
  • 批准号:
    9970673
  • 财政年份:
    1999
  • 资助金额:
    $ 57.5万
  • 项目类别:
    Standard Grant
Dynamical Systems and Smooth Ergodic Theory
动力系统和平滑遍历理论
  • 批准号:
    9803150
  • 财政年份:
    1998
  • 资助金额:
    $ 57.5万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Dynamical Systems Conference
数学科学:动力系统会议
  • 批准号:
    9531653
  • 财政年份:
    1996
  • 资助金额:
    $ 57.5万
  • 项目类别:
    Standard Grant
FAW: Mathematical Sciences: Chaotic Dynamics
一汽:数学科学:混沌动力学
  • 批准号:
    9696200
  • 财政年份:
    1996
  • 资助金额:
    $ 57.5万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Dynamical and Related Topics
数学科学:动力学及相关主题
  • 批准号:
    9504863
  • 财政年份:
    1995
  • 资助金额:
    $ 57.5万
  • 项目类别:
    Continuing Grant

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