复动力系统

探讨了复动力系统迭代生成拟3D分形图像的几种简单技巧。

Several simple methods are proposed to generate pseudo 3D fractal images .

复动力系统生成的拟3D分形图像

Pseudo-3D Fractal Images Generated by Complex Dynamical Systems

在第二章中，研究二次多项式z~2+cn生成的随机复动力系统的Julia集的拓扑学性质，解决了R。

In chapter 2 , we study topological properties of Julia sets for the random dynamical system generated by z2 + cn and answer a question posed by R.

本文针对复动力系统广义Julia集、最基本Julia集和三角函数Julia集，以及一类空间Julia集，创新性地解决了复动力系统分形的辨识控制问题。

In this paper , the identification control on fractal of the complex dynamic sys-tems which include the generalized Julia sets , basic Julia sets , trigonometric function Julia sets and one class of spatial Julia sets , is innovatively achieved .

在第一章中，讨论二次多项式z~2+cn生成的复动力系统的Julia集完全不连通的条件。并且给出了一个例子。

In chapter 1 , we discuss the condition for Julia sets for the random dynamical system generated by the quadratic polynomials z2 + cn to be totally disconnected , and construct a sequence ( cn ) for which the Julia set J ( cn ) is totally disconnected .

利用李雅普诺夫指数分析了两个复动力系统的混沌模型，一个是Mandelbrot集，另一个是伊侬映射，进而探讨了这两个模型在什么情况下从有序进入混沌状态。

Based on Yaupon-Exponent , two kinds of chaos model , one is Mandelbrot set , another is Henon mapping , is analyzed . Father more for these two model how to get from orderly state to chaos is studied .

本文的第二章主要研究多个函数的特定迭代序列，讨论了高次多项式的随机复动力系统的Julia集的连通的充分必要条件以及稠密性问题，同时还讨论了一类多项式函数的Mandelbrot集。

Chapter two study iteration of a serial of polynomial , discussed the sufficient and necessary conditions and denseness of the Julia set , the relative random dynamical system is constructed by some high degree polynomial . In addition , it discuss the Mandelbrot set of a kind of polynomial .

复动力系统生成分形图形算法研究

On the Algorithm of Fractal Image form Complex Dynamic System

随机复动力系统若干问题的研究

Studies on Topics for the Random Dynamical System

对随机复动力系统的研究现在主要有两个不同的研究方向：研究多个函数的所有迭代序列的动力学性质和研究多个函数的特定迭代序列的动力学性质。

Now studying of random dynamical system has two direction : Studying the iteration of a serial and studying the iteration of all serials .

今天的动力系统大致可分为微分动力系统、拓扑动力系统、无穷维动力系统、复动力系统、遍历论等方向。

Roughly speaking , dynamical systems consist of differential dynamical system , topological dynamical system , infinite dimensional dynamical system , complex dynamical system and ergodic theory etc.

非线性复动力系统的迭代可以产生十分复杂的现象，分形与混沌就是其中的两个典型问题，并且二者具有密切的联系。

The iteration of nonlinear complex dynamical system can make very com-plicated phenomenon , and Fractals and Chaos are two typical problems in the nonlinear system while they are closely related .

介绍了非线性随机动力学的响应、分岔、混沌以及混沌同步与控制的研究现状和发展趋势，探讨了随机复动力系统、时滞系统、逼近方法和数值方法研究中的若干问题及其进展。

Based on the recent situation and trend of the nonlinear systems , we present some recent developments and important problems in stochastic dynamics such as response , bifurcation , chaos , synchronization and control .

实验结果表明，该算法通过扰动控制和变形控制共12个参数的引入，实现了对复动力系统分形集整体结构和局部细节的有效控制，且算法具有简单、快速和可控强的优点。

The experimental results show that the algorithm can expediently control the integral structures and local details of the fractal sets generated from complex dynamical systems when 12 perturbative and deformation parameters are interactively adjusted . The algorithm is simple , fast and easy to control .

次数大于2的多项式的随机复解析动力系统的JULIA集的连通性

Connectedness of Julia sets for the random dynamical system generated by polynomials of degree ≥ 2

研究了一类有理函数构成的随机动力系统，得到该系统的Julia集和Fatou集，证明了随机动力系统和经典的复解析动力系统之间有一些本质的差异。

We study a random dynamical system formed by a set of rational functions , obtaining Julia set and Fatou set of this system . And it is proved that there exists some essential difference between the random dynamical system and the classical analytic dynamical system .

复解析动力系统发展概况

Recent Developments of Complex Analytical Dynamic Systems

对动力系统的研究是目前非线性科学领域中最活跃的部分，关于复形式离散动力系统的研究在不断深入，特别是研究参数空间上由各种不同周期的双曲分量构成的Mandelbrot集的结构。

Researches into dynamics are presently the most active parts in the field of nonlinear science , and many advances have been made in the researches into complex separated dynamics , especially in the structures of the M set formed by hyperbolic components with various periods .

对复域混沌动力系统作出了构建示例。

Give a construct example of chaos dynamic system in complex field .

复系数离散动力系统的稳定性

The Stability of Dynamical Systems of Complex Coefficients