实指数幂多元牛顿变换的Julia集  

Julia sets of multivariable Newton transform for real exponent power

作　　者：王兴元[1] 王婷婷[1] 

机构地区：[1]大连理工大学电子与信息工程学院,辽宁大连116024

出　　处：《大连理工大学学报》2007年第6期897-903,共7页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(60573172);辽宁省教育厅高等学校科学技术研究资助项目(20040081)

摘　　要：阐述了多元牛顿变换的Julia集理论,给出了多元牛顿迭代法,推广了Motyka和Reiter的工作,构造并研究了实指数幂多元牛顿变换的Julia集.结果发现:随参数β值增大,实指数幂多元牛顿变换的Julia集有一个突变,表现为吸引域的个数加1;多元牛顿变换Julia集的吸引域的结构取决于初始点的选取;实指数幂多元牛顿变换Julia集的结构,依赖于相角θ主值范围的选取;多元牛顿变换的Julia集具有对称性.The theory of Julia sets on multivariable Newton transform is introduced, and the multivariable Newton iteration method is given to extend the work of Motyka and Reiter by the construction and analysis of the Julia sets of multivariable Newton transform for real exponent power. The results show that as the value of the parameter β increases, the Julia sets of the multivariable Newton transform have a sudden change caused by the increase of the attraction region. The structure of attraction region of the Julia sets of multivariable Newton transform depends on the selection of the initial value. The structure of the Julia sets of the multivariable Newton transform for real exponent power depends on the selection of the principal value of the phase angle θ. The Julia sets of multivariable Newton transform have a symmetrical character.

关 键 词：多元牛顿变换 JULIA集 突变 相角 对称性 

分 类 号：TP301.5[自动化与计算机技术—计算机系统结构]