Fractal Structures of General Mandelbrot Sets and Julia Sets Generated From Complex Non-Analytic Iteration Fm (z) =-zm + c
In this paper we use the same idea as the complex analytic dynamics to study general Mandelbrot sets and Julia sets generated from the complex non-analytic iteration.The definition of the general critical point is given,which is of vital importance to the complex non-analytic dynamics.The general Mandelbrot set is proved to be bounded,axial symmetry by real axis,and have (m+(l))-fold rotational symmetry.The stability condition of periodic orbits and the boundary curve of stability region of one-cycle are given.And the general Mandelbrot sets are constructed by the escape-time method and the periodic scanning algorithm,which present a better understanding of the structure of the Mandelbrot sets.The filled-in Julia sets Km,c have m-fold structures.Similar to the complex analytic dynamics,the general Mandelbrot sets are kinds of mathematical dictionary or atlas that map out the behavior of the filled-in Julia sets for different values of c.
Complex Non-analytic Iteration Critical Point General Mandelbrot Set Julia Set
Yan Dejun Wei Xiaodan Zhang Hongpeng Jiang Nan Liu Xiangdong
Research Institute of Non-linear Information Technology Dalian Nationalities University Dalian 116600, P.R.China
国际会议
太原
英文
167-170
2013-04-06（万方平台首次上网日期，不代表论文的发表时间）