Extended escaping set for meromorphic functions outside a countable set of transcendental singularities
Volume 129 / 2022
Annales Polonici Mathematici 129 (2022), 25-41
MSC: Primary 37F10; Secondary 30D30.
DOI: 10.4064/ap190820-31-3
Published online: 20 June 2022
Abstract
We consider the class $\mathcal K $ of functions $f$ that are meromorphic outside a compact and countable set $B(f)$, which is the closure of isolated transcendental singularities of $f$. We define the extended escaping set $\widehat I (f)$ and prove that $\widehat I (f)$ is a dynamical invariant. Using curves contained in $\widehat I (f)$ we define the itinerary of an escaping curve for transcendental singularities. As an example we study the function $f(z)=e^{\frac {1}{\sin z}}+z+2\pi $ and show that it has an escaping curve contained in a wandering domain with a wandering end-point.
