映射

The condition for a 3D polynomial map to be equivariant is theoretically analyzed and proved.

研究了基于三维多项式映射的三维广义Julia集表示方法。

Complicated system ; fractal ; nonlinear dynamics ; Mandelbrot set ; Julia set ; extension factor ; ternary number ; period-checking algorithm ; volume rendering algorithm ; equivariant map ; chaotic dynamic system ; synthesis of mechanism

国家自然科学基金；国家重点基础研究发展计划(973计划)复杂系统；分形；非线性动力学；可视化； Mandelbrot集； Julia集；变形伸缩因子；三元数；周期检测法；体绘制算法；等变映射；混沌动力系统；机构综合

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。

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。

In this paper, we study the existence and ergodicity on invariant measures of set-valued mappings.

中文摘要：在这篇文章里，我们研究了集值映射不变测度的存在性和遍历性。

Chaotic mappings have the features of initial-value sensitivity, ergodicity and randomicity, and are greatly fit for information encryption.

混沌映射具有初值敏感性、遍历性和伪随机性的特点，很适合用于信息加密。

It was found that there's definite product relationship between the iteration times m and the corresponding critical equivalent coefficient error.

特别地，对带有迭代若干次的充分伸展的Marcov映射的混沌加密系统，其迭代次数m与相应的临界等效系数误差间存在明确的倍数关系。

From the model, functional relationship between kinematics reliability of tool tip and every error resources was got; the contribution of each error component to the kinematics accuracy of the mechanism was analyzed and the key of all error resources was confirmed.

应用误差模型能够得出末端执行器位姿误差和各个误差源之间的显式映射关系，定量地分析各个误差源对机构运动精度的影响程度，从而确定机构中影响其运动精度的关键环节。

In particular ,for the path associated with k points, what is the structure of image of the Laplacian Eigenmap in 2-dimensional Euclidean space.

比如说，在二维的Euclidean空间中的拉普拉斯特征映射的像的构造是由k个点连结的路Pk 。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。