马蹄映射 Cantor 分形图计算机构造及其混沌分维特性

Computer Construction of Horseshoe Map Cantor Fractal Graphic and Specific Property of Chaos Fractal Dimension

马蹄映射是具有无穷多个周期点的结构稳定（或Ω稳定）的混沌动力学研究中第一个经典型例子．计算机构造出自相似马蹄映射，并实现了升腾变换，提供了马蹄映射的高维动力性态，并据此计算出马蹄映射Ｃａｎｔｏｒ分形图的混沌分维．本算法理论上适用于ｎ次迭代．同时，马蹄映射产生的Ｃａｎｔｏｒ分形图与Ｍａｎｄｅｌｂｒｏｔ集和Ｊｕｌｉａ集以及其它一些分形图，虽然正式地看来是决定论的后果，实质上可看作一个随机过程的极限．

Horseshoe map is the first example of stable structure which has endless periodic points. Computer algorithmas are used to construct a selfsimilar horseshoe map and the lifted horseshoe map. These algorithms describe the orbit of the horeshoe map,and calculate the fractal dimension. These algorithms could iterate for n times.