【摘要】 给出了周期点分类构造Julia集的算法,克服用逃逸时间算法和反函数迭代法构造复映射族f(z,c)=z-2+cJulia集收敛不均匀的问题·研究了z-2+c不同参数对应Julia集的拓扑结构的演变规律,发现了不同性质的周期芽苞的点对应的Julia集的不同属性,给出了通过Julia集判断参数类型和通过参数位置预知Julia集拓扑结构的方法·提出了关于Julia集的连通性的一个猜想,并用大量计算机实验支持了这一猜想·更多还原

【Abstract】 ?A new method,periodclassification algorithm,to get a better graphic of Julia sets of complex mapping z-2+c was given. Comparing with other algorithms such as escape time algorithm and inverse function algorithm, the periodclassification algorithm provides a better understanding of the dynamics of the complex mapping z-2+c. A large numbers of Julia sets of z-2+c were exhibited by use of a computer. Periodbuds were classified and the difference of the Julia sets in deferent periodbuds was studied. The period of the Julia set can be found and also the topological structure of the Julia set can be predicted by observing the position of the periodbud. A conjecture that all the Julia sets with 2 or higher periods are connected is presented. The conjecture is proved by lots of computer experiments.更多还原