On the formulas of meromorphic functions with periodic Herman rings

We construct some explicit formulas of rational maps and transcendental meromorphic functions having Herman rings period strictly larger than one. This gives an answer to a question raised by Shishikura in the 1980s. Moreover, with nested are also found. To obtain periodic rings, crucial step is find family entire bounded Siegel disks all possible periods rotation numbers. based on proving existence Mandelbrot-like set one corresponding parameter space.