ERGODIC-THEORY OF CHAOS AND STRANGE ATTRACTORS
ERGODIC-THEORY OF CHAOS AND STRANGE ATTRACTORS
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DOI：
10.1103/revmodphys.57.617
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发表时间：
1985-01-01
影响因子：
44.1
通讯作者：
RUELLE, D
中科院分区：
文献类型：
--
作者：
ECKMANN, JP;RUELLE, D
物理和数值实验表明，确定性噪声或混沌是无处不在的。虽然已经取得了很好的理解的混沌的发病，作为一个数学工具，可微动力系统的几何理论，适度激发混沌系统需要新的工具，这是由动力系统的遍历理论提供。这一理论已经达到了一个阶段，与物理实验的富有成效的接触和交流已经变得广泛。本文介绍了分析实验的主要数学思想及其具体实现。主要科目是维数理论（激发自由度的数量），熵（信息的产生）和特征指数（描述对初始条件的敏感性）。这些数量之间的关系，以及它们的实验测定，进行了讨论。这些数量的系统调查为我们提供了第一次与动力系统，激发远远超出准周期制度的合理理解。这是理解高度湍流流体的又一步。
Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the geometric theory of differentiable dynamical systems, moderately excited chaotic systems require new tools, which are provided by the ergodic theory of dynamical systems. This theory has reached a stage where fruitful contact and exchange with physical experiments has become widespread. The present review is an account of the main mathematical ideas and their concrete implementation in analyzing experiments. The main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions). The relations between these quantities, as well as their experimental determination, are discussed. The systematic investigation of these quantities provides us for the first time with a reasonable understanding of dynamical systems, excited well beyond the quasiperiodic regimes. This is another step towards understanding highly turbulent fluids.