含参有理函数族M集的拓扑不变特性

Investigation on the Fixed Topological Characters of the M Set of the One Parameter Rational Functions

利用Ｎｅｗｔｏｎ 法对应的有理函数族给出一系列新的广义Ｍａｎｄｅｌｂｒｏｔ 集和Ｊｕｌｉａ 集，通过计算机研究了它们与典型Ｍａｎｄｅｌｂｒｏｔ 集和Ｊｕｌｉａ 集之间的关系，并对Ｍａｎｄｅｌｂｒｏｔ 集与Ｊｕｌｉａ 集之间的关系进行了分析，解析分析了广义Ｍａｎｄｅｌｂｒｏｔ 集的有界性、芽苞周期和不同周期芽苞个数，为Ｍａｎｄｅｌｂｒｏｔ 集和Ｊｕｌｉａ 集的发展提供了新的思路·

A series of general Mandelbrot sets of the rational functions with one parameter coming from Newton's method were constructed. The relationship between the general Mandelbrot sets and the common Mandelbrot sets was discussed. The boundaries of these general Mandelbrot sets and two formulas for calculating the number of period of general Mandelbrot sets were given out. A new way was provided to develop the Mandelbrot and Julia sets.