Mandelpinski Rings around Sierpinski Holes

In recent years, the theory of complex dynamics has attracted a lot of attention due to the important role that they play in various fields of applications.In this book, we study the Mandelpinski structure in the parameter plane of McMullen family. Mandelpinski structure is usually described as a certain fractal structure associated with baby Mandelbrot sets and Sierpinski holes in the parameter plane of McMullen family. There have been discovered many Mandelpinski structures such as Mandelpinski ring, Mandelpinski spokes and Mandelpinski maze. Mandelpinski ring is a curve passing thorough the centers of baby Mandelbrot sets and Sierpinski holes alternately. We construct a new fractal structure in the dynamical plane and parameter plane of McMullen family. This structure consists of many simple closed curves lying around Sierpinski holes and passing through special parameters such as superstable parameters and escape parameters.