We show that the set of λ-values for which λ exp(z)does not have stable regions has Hausdorff dimension two,and that the set of λ-values for which λ sin(z)does not have stable regions has a positive area.
为构造出负整数次幂复映射族f(z)=z^(-n)+c的新型分形,研究了利用该复映射族的广义M集的1周期参数构造非线性迭代函数系的方法.根据广义M集的对称性,选定正实轴上方与正实轴成π/(n+1)角度内的M集中1周期参数区域为构造IFS(Iterated Fun...为构造出负整数次幂复映射族f(z)=z^(-n)+c的新型分形,研究了利用该复映射族的广义M集的1周期参数构造非线性迭代函数系的方法.根据广义M集的对称性,选定正实轴上方与正实轴成π/(n+1)角度内的M集中1周期参数区域为构造IFS(Iterated Function Systems,函数迭代系)中压缩迭代函数的参数源区域;试验选取2个或以上参数构造非线性压缩IFS,并构造分形.根据完整M集的1周期参数区域的对称特点,在参数源区域挑选多个参数,将每个参数扩展到n+1个旋转对称参数或2(n+1)个旋转对称和反射对称参数,由这些参数构造出相应的迭代函数,组成一个非线性的IFS,并构造出对称分形.实验结果表明,用本文方法构造的非线性IFS,可以用复映射族f(z)=z^(-n)+c构造出大量的结构各异的新颖分形.展开更多
文摘We show that the set of λ-values for which λ exp(z)does not have stable regions has Hausdorff dimension two,and that the set of λ-values for which λ sin(z)does not have stable regions has a positive area.
文摘为构造出负整数次幂复映射族f(z)=z^(-n)+c的新型分形,研究了利用该复映射族的广义M集的1周期参数构造非线性迭代函数系的方法.根据广义M集的对称性,选定正实轴上方与正实轴成π/(n+1)角度内的M集中1周期参数区域为构造IFS(Iterated Function Systems,函数迭代系)中压缩迭代函数的参数源区域;试验选取2个或以上参数构造非线性压缩IFS,并构造分形.根据完整M集的1周期参数区域的对称特点,在参数源区域挑选多个参数,将每个参数扩展到n+1个旋转对称参数或2(n+1)个旋转对称和反射对称参数,由这些参数构造出相应的迭代函数,组成一个非线性的IFS,并构造出对称分形.实验结果表明,用本文方法构造的非线性IFS,可以用复映射族f(z)=z^(-n)+c构造出大量的结构各异的新颖分形.
