Mathematical Sciences: Scientific Conference on Hamiltonian Dynamical Systems

数学科学：哈密顿动力系统科学会议

• 批准号: 9120524
• 负责人: Kenneth Meyer
• 金额: $ 0.9万
• 依托单位: University of Cincinnati Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-03-01 至 1993-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9120524&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Scientific; Conference; Hamiltonian

From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics. The power and elegance of Hamiltonian methods were first seized upon in the mid-nineteenth century by theoretical astronomers, who reduced problems in their discipline to the task of finding enough "integrals" of an appropriate Hamiltonian system; these integrals were difficult to find except for the simplest systems. Poincare showed that the emphasis should not be placed on solving the equations for a physical system, but rather that the important features of a system's behavior could be found by other means. These new methods had a strong effect on mathematics itself, as the fields of topology and dynamical systems arose out of Poincare's qualitative, geometric vision of problems in celestial mechanics and Hamiltonian systems. The qualitative approach to dynamical systems has remained an active research area, especially now that computers provide a "laboratory" in which to view systems of increasing complexity. Driven partly by the discovery in these experiments of new phenomena and partly by the maturation of the mathematical disciplines arising out of Poincare's work, the results and methods of Hamiltonian systems have grown and penetrated neighboring fields of research. This project will support an International Conference on Hamiltonian Dynamical Systems to be held from March 25-28, 1992 at the University of Cincinnati. The conference will gather together leading and newer researchers to discuss the latest results in Hamiltonian systems and its applications, and to gain an overview of how those results relate to each other and to the discipline as a whole. To emphasize the comprehensive aspect of the conference, at least one of the plenary speakers will be a professional historian of science, and will discuss the subject in the broadest possible terms.

从近两个世纪前的起源开始，哈密顿动力学已经发展到涵盖几乎所有不耗散演化系统的物理学，以及许多数学分支。 哈密​​顿方法的力量和优雅首先在十九世纪中叶被理论天文学家抓住，他们将学科中的问题简化为寻找合适的哈密顿系统的足够“积分”的任务；除了最简单的系统之外，很难找到这些积分。 庞加莱表明，重点不应该放在求解物理系统的方程上，而应该通过其他方式找到系统行为的重要特征。 这些新方法对数学本身产生了强烈的影响，因为拓扑和动力系统领域源于庞加莱对天体力学和哈密顿系统问题的定性、几何视野。 动力系统的定性方法仍然是一个活跃的研究领域，特别是现在计算机提供了一个“实验室”来观察日益复杂的系统。 部分是由于这些实验中新现象的发现，部分是由于庞加莱工作所产生的数学学科的成熟，哈密顿系统的结果和方法已经发展并渗透到邻近的研究领域。 该项目将支持将于 1992 年 3 月 25 日至 28 日在辛辛那提大学举行的哈密顿动力系统国际会议。 会议将聚集领先和新的研究人员，讨论哈密顿系统及其应用的最新结果，并概述这些结果如何相互关联以及与整个学科的关系。 为了强调会议的综合性，全体会议发言者中至少有一位将是专业的科学史家，并将尽可能广泛地讨论该主题。