GLOBAL ANALYTICAL STRUCTURE OF THE MANDELBROT SET AND ITS GENERALIZATION | |
HUANG, YN | |
刊名 | science in china series a mathematics physics astronomy |
1992 | |
关键词 | MANDELBROT SET STABLE PERIODIC ORBITS CONFORMAL MAPPING |
英文摘要 | In this paper we study the global structure of periodic orbits for a one-dimensional complex map Z(n+1) = Z(n)m + C by the algebraic analytical method advanced by the author in 1985. We give a general formula for the calculation of the orbit number H(N) of any period-N orbit. We also verify rigorously that the complex structures of the Mandelbrot set (m = 2) and its generalized form (m > 2) are composed of infinitely many stable regions of different periodic orbits. We find out that the relation between the stable region number I(N) of the period-N orbit and its orbit number H(N) is exactly I(N) = N . H(N)/m. The algebraic equations of the boundary of each element and the locations of its cusp and center can be given precisely. Furthermore, the cause of the infinitely nested structures for these complex figures are explained.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992HK81800006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics, Applied; Mathematics; SCI(E); 0; ARTICLE; 2; 175-185; 35 |
语种 | 英语 |
内容类型 | 期刊论文 |
源URL | [http://ir.pku.edu.cn/handle/20.500.11897/316274] |
专题 | 工学院 |
推荐引用方式 GB/T 7714 | HUANG, YN. GLOBAL ANALYTICAL STRUCTURE OF THE MANDELBROT SET AND ITS GENERALIZATION[J]. science in china series a mathematics physics astronomy,1992. |
APA | HUANG, YN.(1992).GLOBAL ANALYTICAL STRUCTURE OF THE MANDELBROT SET AND ITS GENERALIZATION.science in china series a mathematics physics astronomy. |
MLA | HUANG, YN."GLOBAL ANALYTICAL STRUCTURE OF THE MANDELBROT SET AND ITS GENERALIZATION".science in china series a mathematics physics astronomy (1992). |
个性服务 |
查看访问统计 |
相关权益政策 |
暂无数据 |
收藏/分享 |
除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。
修改评论