就康托尔集讨论混沌与分形的内在联系物理学

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东北师范大学本科毕业论文

就康托尔集讨论混沌与分形的内在联系学生姓名：张艳娇指导教师：肖青老师所在学院：物理学院所学专业：物理学中国·长春 20 13 年 5 月

东北师范大学本科毕业论文

就康托尔集讨论混沌与分形的内在联系············································1 目录··········································································2 摘要··········································································3 关键字·······································································3 Abstract······································································4 Keywords ·····································································4 引言··········································································5 混沌的介绍····································································6 定义········································································6 特征········································································6 分形介绍······································································7 数学定义·····································································7 几何艺术美···································································8 康托尔集中的混沌与分形·······················································11 介绍·······································································11 康托尔三分集构造····························································12 性质特点····································································12 结束语·······································································13 参考文献·····································································14

东北师范大学本科毕业论文

摘要

混沌与分形的理论研究已成为21世纪一个具有明确研究对象和基本课题、独特的概

念体系和方法论框架的学科。随着各个科学方面相关理论的不断完善，有关混沌、分形的理解和研究也更加深入。混沌与分形理论的关系十分密切，混沌中有时包容有分形，而分形中有时又孕育着混沌。分形注重几何形态或几何特性，几何图形的描述，更看重有自相似性的系统而混沌更偏重数理的动力学及动力学与图形结合的多方位的描述研究并且混沌涉及面似乎更广，对所有的有序与无序，有序与有序现象都感兴趣。但是，目前在世界上要较详细、较系统地阐明分形与混沌的关系及差异，还是比较困难,还有待混沌与分形理论进一步的深入研究拓展，完善和趋细。而康托尔集是位于一条线段上的一些点的集合，具有许多显著和深刻的性质，且既能产生混沌又具有分形特征，通过考虑这个集合，我们可以很好的把混沌、分形统一起来。

关键词：混沌理理论、分形理论、康托尔集

东北师范大学本科毕业论文

Abstract

Research on chaos and fractal in 21st century has become clear the object of study and basic subjects, a unique system and methodology framework of the concept of disciplines.With the continuous improvement of all scientific theories, the understanding and study on chaos and fractal more in-depth. Chaos and Fractal theory is very closely related, sometimes, a fractal inclusion in the chaotic and sometimes bred in the fractal chaos.More about geometry or geometry of fractal characteristics, describes the geometry and more a system of self - similarity and Kinetics and dynamics of chaotic more mathematical and graphic description of the multidimensional study on the integration and chaos which seems to be more widely of all ordered and unordered, ordered and ordered interested in.However, at present, to be more detailed than the system to clarify the relation and difference of fractal and chaos, and difficult it remains to be seen further into chaos and Fractal theory to expand, improve and become light.While the cantor set is a collection of some of the points are located on a line segment with many significant and profound in nature, and can produce chaotic and fractal characteristics, by considering this collection, we can unify great chaos and fractal.

Keywords : Chaos Theory and Fractal theory, Cantor set of points

东北师范大学本科毕业论文

引言

混沌与分形理论的产生不仅促进了非线性科学的诞生,还更多的涉及到了其他学科。在

不断的研究混沌与分形理过程中发现了一些重大发现, 这些重大的发现不仅开拓了科学家们的视野和思路, 同时又带来了一些未知的问题。混沌和分形理论的建立，进一步改变了人们对这个世界的看法，混沌与分形把简单与复杂、有序和无序、稳定与不稳定、确定和随机等矛盾体统一在了一幅美丽的自然画卷里。混沌理论与分形的近代研究，已经应用到了各个领域，它们从另一极端对传统科学提出了严峻的挑战，同时又给传统科学提供了天然的弥补和深刻的启示，启发着新时代的科学家不断不断与时俱进！

面对新时代和新形势，混沌与分形已经变成一项代表重塑科学体系的狂飙运动，混沌与分形理论正在21世纪科学界蓬勃发展着，它们将会开启世界科学的新纪元。