On multiply connected wandering domains of entire functions

On the Uniform Perfectness of the Boundary of Multiply Connected Wandering Domains

“…We use Theorem 1.2 to show that in Baker's original example of a multiply connected wandering domain, that is, the example given by (1.1) and (1.2), the connectivity is infinite and the boundary is not uniformly perfect. The question whether the connectivity of this domain is finite or infinite was raised by Baker [5] and by Kisaka and Shishikura [12]; the question was repeated in [8, p. 2946] and [16, p. 312].…”

Fatou components whose boundaries have a common curve

“…Similarly, we define h − n (t) by interchanging + and − in the definition of h + n (t). By an argument and a calculation similar to those in [5], there exist functions h + (t) and h − (t) and t 0 > 0 such that h + n (t) → h + (t) and h − n (t) → h − (t) uniformly on compact subsets of {t | t ≥ t 0 }. In addition, (1) lim t→∞ |h ± (t)| = ∞, (2) lim n→∞ |f n (h ± (t))| = ∞ for all t ≥ t 0 and (3) h ± (t) is injective with respect to t. We denote {h + (t) | t ≥ t 0 } and {h − (t) | t ≥ t 0 } by H + and H − , respectively.…”

“…Ray tails for exponential maps have been considered by many authors, for example, [2] and [11]. In [5], Kisaka considered ray tails for structurally finite transcendental entire functions.…”

Dynamics of Entire Functions

“…Baker wandering domains may have any connectivity, finite or infinite [KS08] (the eventual connectivity will be 2 or ∞). These may coexist with simply connected wandering domains [Be].…”

“…Modifying the construction for small values of n, they obtain Baker wandering domains with any finite, or with infinite connectivity (as well as with many further properties; see [KS08,Be]). …”