一个非解析复映射的广义Julia集

数学物理学报 ›› 2005, Vol. 25 ›› Issue (7): 1030-1039.

一个非解析复映射的广义Julia集

王兴元, 骆超

大连理工大学电子与信息工程学院大连 |116024

出版日期:2005-12-30 发布日期:2005-12-30
基金资助:
国家自然科学基金(69974008)及辽宁省教育厅高等学校科学技术研究计划(20040081)资助

Generalized Julia Sets From a Nonanalytic Complex Mapping

WANG Xin-Yuan, Luo Chao

Online:2005-12-30 Published:2005-12-30
Supported by:
国家自然科学基金(69974008)及辽宁省教育厅高等学校科学技术研究计划(20040081)资助

摘要/Abstract

摘要：

推广了Michelitsch和Rossler所提出的由一个简单非解析映射所构造Julia集的方法,并由推广的复映射,构造出一系列实数阶的广义Julia集(简称广义J集)．
利用复变函数理论和计算机制图相结合的实验数学的方法,对广义J集的结构和演化进行了研究,结果表明：

①广义J集的几何结构依赖于参数α、R和c;

②广义J集具有对称性和分形特征;

③小数阶广义J集出现了错动和断裂,且其演化过程依赖于相角主值范围的选取.

关键词: 非解析映射;广义J集;分形;演化

Abstract:

The method constructing the Julia sets from a simple nonanalytic mapping developed by Michelitsch and Rossler is expanded. According to the complex mapping expanded by the author, a series of the generalized Julia sets for real index number are constructed. Using the experimental mathematics method and combining the theory of analytic functions of one complex variable with computer aided drawing, the fractal features and evolutions of the generalized Julia sets are studied. The results show: (i) the geometry structure of the generalized Julia sets depends on the parameters of α,R and c; (ii) the generalized Julia sets have symmetry and fractal feature; (iii) the generalized Julia sets for decimal index number have discontinuity and collapse, and their evolutions depend on the choice of the principal range of the phase angle.

Key words: Nonanalytic mapping, The generalized Julia sets, Fractal, evolution

中图分类号:

28A80

王兴元, 骆超. 一个非解析复映射的广义Julia集[J]. 数学物理学报, 2005, 25(7): 1030-1039.

WANG Xin-Yuan, Luo Chao. Generalized Julia Sets From a Nonanalytic Complex Mapping[J]. Acta mathematica scientia,Series A, 2005, 25(7): 1030-1039.

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