遍历理论

Investment share ; market share ; portfolio ; random dynamical system ; multiplicative ergodic theorem

投资份额；市场份额；资产组合；随机动力系统；乘积遍历理论

In chapter 2, some preliminary kownledges in topologically dynamical system and ergodic theory, which will be used in this paper, are reviewed.

在第二章中，我们介绍了本文涉及到的一些拓扑动力系统和遍历理论的预备知识。

In the first chapter we introduce the basic notions and results of topological dynamics, including some basic knowledge of ergodic theory which will be used in context.

在第一章中，我们简要的介绍了本文涉及到的拓扑动力系统与遍历理论的一些基本概念与结论。

It is wellknown, composition of functions is a fundamental operation in all mathematics and has been studied for a long time, for example, in the iteration of rational functions and in the ergodic theory.

事实上函数的复合是数学各个分支上的一种基本运算，且有悠久的历史，例如有理函数的迭代或可测函数空间上的遍历理论问题。

These sets are interesting subsets of natural number in combinatorial number theory, ergodic theory and topological group.

这些集合是人们在组合数论、遍历理论以及拓扑群中感兴趣的重要的自然数子集。

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。

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。

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。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。