Herman Rings: Structure, Dynamics, and Open Problems

Abstract

The existence of the Herman ring of a function adds interest and complexity to the dynamics of the function. We present a detailed and understandable summary of the core discoveries and recent developments on the Herman ring of rational and transcendental meromorphic functions. It is demonstrated that the Herman ring is intriguing on its own and valuable in terms of overall dynamics. Finally, the results and potential future research problems are briefly discussed.