摘要
基于作者提出的开关复映射 ,阐述了开关广义Mandelbrot集 (简称开关广义M集 )的构造方法 ,并构造出一系列复数阶的开关广义Mandelbrot集· 通过分析广义M集的构造算法 ,阐述了广义M集的结构特点· 在此基础上对在开关映射作用下复C平面上初始点的轨道进行了研究 ,发现开关广义M集具有分形结构 ,其结构特征依赖于复指数w及开关变量r0 ,其断裂的原因是主幅角选取的不连续性·
According to the switched complex mapping proposed by the author,the method constructing the switched processes generalized M(Mandelbrot)sets was elaborated,and a series of the switched processes generalized M sets for complex index number were constructed.The construction characteristics of the generalized M sets were expounded according to the analysis of the algorithm constructing the generalized M sets.On the basis of what has already been achieved,the trajectories of a starting point in the complex C_plane under the switched mapping were researched into.The results show that the switched processes generalized M sets have the fractal feature, the construction characteristics of the switched processes generalized M sets are dependent on the complex index number w and the switched variable r 0,and the reason which results in the discontinuity of the switched processes generalized M sets is the discontinuity of choice of the principal range of the phase angle.
出处
《应用数学和力学》
EI
CSCD
北大核心
2003年第1期67-73,共7页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目 (6 9974 0 0 8)
中国博士后科学基金
辽宁省自然科学基金资助项目 (972 194 )
