Mayer, Volker; Urbański, Mariusz Exponential elliptics give dimension two. (English) Zbl 1075.30018 Ill. J. Math. 49, No. 1, 291-294 (2005). Summary: Using the theory of infinite iterated function systems, we show that the Julia set of any function of the type \(G=\lambda\exp \circ F\), \(\lambda \in \mathbb C \setminus \{0\}\), with \(F:\mathbb C \to \widehat C\) a non-constant elliptic function, has Hausdorff dimension two. However, there exist elliptic functions \(F\) such that the Julia sets of the maps \(G=\exp \circ F\) are nowhere dense in \(\mathbb C\). MSC: 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable × Cite Format Result Cite Review PDF