Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag
Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag
复制标题
DOI：
10.1007/978-1-4684-0313-8
复制
发表时间：
1993-09
期刊：
影响因子：
--
通讯作者：
R. Temam
中科院分区：
文献类型：
--
作者：
R. Temam
非线性动力学的研究是一个引人入胜的问题，它是理解自然科学中许多重要问题的核心。非线性动力学中最古老和最著名的两类问题是天体力学问题，特别是对太阳系中物体运动的研究，以及流体中的湍流问题。这两种现象长期以来都引起了科学家们的兴趣；它们很容易观察，并导致我们想要理解的复杂模式的形成和发展。第一类问题的维度是有限的，后一类问题的维度是无限的，这里的维度是描述系统在给定时刻的构型所必需的参数的数量。除了这些外行人和科学家都可以观察到的问题之外，现在还有广泛的非线性湍流现象（有限或无限维），这些现象是从最近的科学和技术发展中出现的，例如化学动力学，等离子体物理学和激光，非线性光学，燃烧，数学经济学，机器人技术，....与线性系统相比，非线性系统的演化遵循复杂的规律，一般来说，这些规律是无法通过纯粹的直觉或基本的计算得到的。
The study of nonlinear dynamics is a fascinating question which is at the very heart of the understanding of many important problems of the natural sciences. Two of the oldest and most notable classes of problems in nonlinear dynamics are the problems of celestial mechanics, especially the study of the motion of bodies in the solar system, and the problems of turbulence in fluids. Both phenomena have attracted the interest of scientists for a long time; they are easy to observe, and lead to the formation and development of complicated patterns that we would like to understand. The first class of problems are of finite dimensions, the latter problems have infinite dimensions, the dimensions here being the number of parameters which is necessary to describe the configuration of the system at a given instant of time. Besides these problems, whose observation is accessible to the layman as well as to the scientist, there is now a broad range of nonlinear turbulent phenomena (of either finite or infinite dimensions) which have emerged from recent developments in science and technology, such as chemical dynamics, plasma physics and lasers, nonlinear optics, combustion, mathematical economy, robotics,.... In contrast to linear systems, the evolution of nonlinear systems obeys complicated laws that, in general, cannot be arrived at by pure intuition or by elementary calculations.