Fixed Points of Commuting Holomorphic Mappings Other than the Wolff Point
نویسندگان
چکیده
Let ∆ be the unit disc of C and let f, g ∈ Hol(∆,∆) be such that f ◦ g = g ◦ f . For A > 1, let FixA(f) := {p ∈ ∂∆ | limr→1 f(rp) = p, limr→1 |f ′(rp)| ≤ A}. We study the behavior of g on FixA(f). In particular, we prove that g(FixA(f)) ⊆ FixA(f). As a consequence, besides conditions for FixA(f)∩FixA(g) 6= ∅, we prove a conjecture of C. Cowen in case f and g are univalent mappings.
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