Bishop's qc-folding and wandering domains in Eremenko ... - ICMS

Multiply-connected wandering domain (Baker 1976)
∏
∞
Let g(z) = Cz
(1 2 + z )
where
a n
n=1
1 < a 1 < a 2 < . . .,
a j+1 < g(a j ) < 2a n+1 ,
g(A j ) ⊂ A j+1 where
A j = {z ∈ C | a 2 j < |z| < √ a j+1 }.
Remark: If A j ⊂ U j then g(U j ) = U j+1 , hence g k (U j ) → ∞ as
k → ∞ for all j.
Theorem (Baker 1975, 1985): If U is a multiply-connected
component of the Fatou set of f then U wanders.
Wandering domains and Bishop’s folding