Julia集及其应用

在以往的有关Julia集的研究中,人们考虑的都是解析函数的迭代。本文考察了由非解析函数迭代生成的M~(?)集,证明了它有类似于Mandelbrot集的一些性质。文中还给出了Julia集在分形几何、迭代函数系、牛顿迭代法、心物学、统计力学等其它一些领域中的应用。作者感谢与S.Bullett博士的有益交谈。

JULIA SETS WITH A VIEW TO APPLICATIONS

In the past, studies on Julia sets were concentrated on the iterates of analytic functions. In this paper, we shall study the M~* sets produced by the iterates of non-analytic functions and prove that M~* has some similar properties as Mandelbrot set. We also give some applications of Julia stes in other fields such as fractal geometry, iterated function systems, Newton's method, psychophysics, statistical mechanics, etc.