遍历

This course introduces the information theory , which employs probability and ergodic theory to study the statistical characteristics of data and communication systems, and the coding theory , which uses mainly algebraic and geometric tools to contrive efficient codes for various situations.

本课程讲授信息论和编码的基本理论。信息论采用概率论和遍历理论的方法研究数据和通信系统的统计特性，编码论主要使用代数和几何等工具为各种应用环境设计有效的编码。

The research of nonlinear ergodic theory began in the mid-seventies. Consequently, it got great development because it was widely used in many questions such as the numerical solution of differential equation, the existence theory of positive solution, control theory, optimization.

非线性算子半群的遍历理论的研究开始于二十世纪七十年代中期，随后由于被广泛应用于微分方程的数值解，正解的存在性理论，控制论，最优化等问题中而得到了很大发展。

This paper discusses Kolmogorov entropy, established to solved the classic problem of the ergodic theory, and topology entropy, advanced to study the topological dynamical system.

介绍了解决遍历理论经典问题的Kolmogorov熵，以及为研究拓扑动力系统而产生的拓扑熵等概念，进而引导读者对这一引人入胜的领域去进行研究。

Furthermore, based on the ergodic theory of Markov process we analyze the stationary distribution of network residual series, and prove the efficient conditions under which the unique asymptotic stationary distribution exists.

同时，根据马氏过程的遍历理论，对网络输出残差的平稳条件进行了研究，证明了网络输出平稳残差的充分条件，给出了残差序列存在唯一的渐近平稳分布的条件。

Nowdays the idea and methods of ergodic theory are applied to studies of various phenomena in statistical physics and condensed matter physics, for example, the Monte-Carlo simulations, critical phenomena, phase transition and anomalous transport.

遍历理论的思想和方法现今正被应用于统计物理和凝聚态物理等的各种现象，如Monte-Carlo、临界现象、相变、反常输运的分析。

Numerical explorations of Henon, Lorenz and others, Mathematical works of Sinai, Bunimovich and Szasz, contributed to the development of modern ergodic theory and chaotic dynamics.

Henon、Lorenz等的数值探索、Sinai、Bunimovich、Szasz等的数学理论工作对现代遍历理论和混沌的研究起了很大的作用。

In chapter 3, on the basis of measure, integration and ergodic theory, it is proved that the statistcal properties and the general complexity of the binary sequences (CG-sequences){b〓} b〓∈{1,-1} generated by a kind of chaos systems and mapping η〓 are as good as white noise sequences. These results lay the foundation of further development.

第三章运用测度、积分以及遍历理论中的一些基本原理，证明了由一类混沌差分系统和映射η〓所产生的二元序列{b〓}，b〓∈{-1，1}，具有与白噪声类似的统计特性和广义复杂度。

After introducing some basic results from ergodic theory, two probIems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system.

首先介绍了遍历理论的一些经典结果；然后着重研究了对应于混沌映射的绝对连续不变测度的存在性与计算问题，这归结于相应的Frobenius-Perron算子的泛函分析与数值分析；最后《确定性系统的统计性质》介绍了Shannon熵、Kolmogorov熵、拓扑熵以及Boltzmann熵，并给出了不变测度的一些最新应用。

According to the Logistic Equation and the impact of stochastic factors, a stochastic nonlinear dynamical model had been presenred. The max Lyapunov exponent was calculated by Oseledec multiplicative ergodic theory, the local stability conditions had been obtained; the global stability conditions had also been obtained by judging the modality of the singular boundary; the stochastic Hopf bifurcation was analyzed using the invariant measure of stable probability density, and the condition of stochastic Hopf bifurcation had been discussed. The key parameter impacting the urban domestic water consumption had been found by numerical emulation.

根据Logistic阻滞增长模型原理，考虑到诸多随机因素的影响，本文建立了一个城市生活用水量的随机非线性模型，运用Oseledec乘性遍历定理计算了模型的最大Lyapunov指数，得到了局部稳定性的条件；通过对扩散边界性态的分析，得到了全局稳定性的条件；通过分析系统平稳状态概率密度的不变测度，得到了模型随机Hopf分岔的条件，结合实际进行了数值仿真，得到了影响用水量的关键参数。

Jiu Ding,Aihui Zhou,Statistical Properties of Deterministic Systems Statistical Properties of Deterministic Systems discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two probIems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation.

摘要本书介绍的是确定性离散动力系统统计性质的基本理论与计算方法，首先介绍了遍历理论的一些经典结果；然后着重研究了对应于混沌映射的绝对连续不变测度的存在性与计算问题，这归结于相应的Frobenius—Perron算子的泛函分析与数值分析；最后本书介绍了Shannon熵、Kolmogorov熵、拓扑熵以及Boltzmann熵，并给出了不变测度的一些最新应用。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。