Mathematical Sciences: Scientific Conference on Hamiltonian Dynamical Systems

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无耗散演化系统的物理学，以及许多数学分支。19世纪中叶，理论天文学家首先利用了哈密顿方法的强大和优雅，他们把自己学科中的问题简化为寻找合适哈密顿系统的足够“积分”的任务；这些积分除了在最简单的系统中很难找到。庞加莱指出，重点不应该放在解决物理系统的方程上，而应该放在系统行为的重要特征可以通过其他方式找到。这些新方法对数学本身产生了强烈的影响，因为拓扑学和动力系统领域是从庞加莱对天体力学和哈密顿系统问题的定性、几何视角中产生的。动力系统的定性方法一直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。部分是由于在这些实验中发现了新的现象，部分是由于庞加莱的工作引起的数学学科的成熟，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。会议将聚集领先的和较新的研究人员，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。为了强调会议的全面性，至少有一位全体会议发言人将是专业的科学历史学家，并将以尽可能广泛的术语讨论该主题。

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.