Abstract:

We give an overview of surgeries by Shishikura to construct rational functions of Herman Rings and state analogous results for transcendental meromorphic functions. We explain in more detail how to generalize one of his surgeries to obtain a transcendental meromorphic function $f$ with a 2-cycle of nested Herman Rings $A$₁ and $A$₂ (where $A$₁ is a subset of the interior of $A$₂) which has no poles in the bounded component of $C\; A$₁.