5 problems

Omitted-value conjecture. A meromorphic function with an omitted value cannot have a Herman ring.

Consider the parameter space of complex Desboves maps with real coefficients. A cycle of attracting Herman rings is a periodic collection of Herman rings whose return dynamics is a…

An invariant circle is a circle preserved by the real rational map under the hypotheses under discussion, and an associated Herman ring is a complex rotational domain containing it…

Nonexistence conjecture for Herman rings. A meromorphic function with a quasi-nested wandering domain has no Herman rings.

Degeneration conjecture. The limit of degenerating Herman rings of bounded type is always a Herman curve.