| 含参有理函数族M集的拓扑不变特性 |
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| 引用本文： | 刘向东,赵雅明,朱伟勇.含参有理函数族M集的拓扑不变特性[J].东北大学学报(自然科学版),1999,20(6):576-579. |
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| 作者姓名： | 刘向东 赵雅明 朱伟勇 |
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| 作者单位： | 东北大学信息科学与工程学院!沈阳110006;鞍山师范学院数学系!鞍山114008;东北大学计算中心!沈阳110006 |
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| 基金项目： | 国家教育部博士点基金，辽宁省自然科学基金 |
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| 摘 要： | 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·
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| 关 键 词： | 临界点 Mandelbrot集 Julia集 |
| 修稿时间： | 1999-04-20 |
Investigation on the Fixed Topological Characters of the M Set of the One Parameter Rational Functions |
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| Liu Xiangdong,Zhao Yaming,Zhu Weiyong.Investigation on the Fixed Topological Characters of the M Set of the One Parameter Rational Functions[J].Journal of Northeastern University(Natural Science),1999,20(6):576-579. |
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| Authors: | Liu Xiangdong Zhao Yaming Zhu Weiyong |
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| Abstract: | 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. |
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| Keywords: | critical point general Mandelbrot set Julia set |
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