Geometric rigidity for class 𝒮 of transcendental meromorphic functions whose Julia sets are Jordan curves

Urbański, Mariusz

doi:10.1090/S0002-9939-09-09918-3

Geometric rigidity for class $\mathcal {S}$ of transcendental meromorphic functions whose Julia sets are Jordan curves
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Proc. Amer. Math. Soc. 137 (2009), 3733-3739 Request permission

Abstract:

We consider any transcendental meromorphic function $f$ of Class $\mathcal {S}$ whose Julia set is a Jordan curve. We show that the Julia set of $f$ either is an extended straight line or has Hausdorff dimension strictly greater than $1$. The proof uses conformal iterated function systems and extends many earlier results of this type.

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