局部有限无穷树上的Mandelbrot瀑布混沌算子

摘要

In this paper, we study Mandelbort cascades associated with independent nonidentically distributed random variable on infinite and locally finite tree. By constructing the random measure, we obtain sufficient conditions for the singularity and the regularity. The Hausdorff dimension of the image measures is estimated. Examples show that the sufficient conditions are not necessary.%本文研究了由局部有限无穷树上的独立不同分布的随机变量所生成的Mandelbrot瀑布混沌算子.通过构造随机测度,得到了判别一般测度的正则性和奇异性的充分条件;计算出了混沌算子的像测度的Hausdorff维数;并举例证明了充分条件不是必要的.