摘要
讨论了Newton方法对应单参数有理函数族的广义Mandelbrot集和Julia集,研究了它们之间的族相似关系,并与zn+c(n∈Z,n≥2)的Mandelbrot集和Julia集之间的族相似关系进行了对比。结果发现Mandelbrot集与Julia集的族相似关系是完全类似的,这一方面说明了参数平面与动力学平面复动力系统间的密切关系,也说明了这种密切关系的普适性,为Mandelbrot集和Julia集的拓展提供了新的思路。
A group general Mandelbrot and Julia sets of the rational functions with one parameter constructed by Newton＇s method are discussed. The relation about the group similarities between the general Mandelbrot sets and Julia sets, and the common Mandelbrot sets and Julia sets of Z^n ＋c （ n ∈ Z, n ≥2） are investigated. It is found that their group similarities between these Mandelbrot sets and these Julia sets are very analogous. This result can be explained that the dynamics on the complex plane have the intimate connection with the dynamics on the parameters plane, so this connection has universality. It gives a new way to improve the theory of the Mandelbrot sets and the Julia sets.
出处
《工程图学学报》
CSCD
北大核心
2008年第6期101-107,共7页
Journal of Engineering Graphics
基金
国家自然科学基金资助项目(60573124)
辽宁省自然科学基金资助项目(20040948)
