3 problems

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

Let $\operatorname{Aut}(\mathbb C^2)$ denote the space of polynomial automorphisms of $\mathbb C^2$. A dynamical system has a wandering Fatou component when it displays a Fatou com…

Rempe-Gillen–Mihaljević-Brandt conjecture. If the orbit of all singular values converges uniformly to infinity in this sense, then $f$ has no wandering domains.