Extended escaping set for meromorphic functions outside a countable set of transcendental singularities
Tom 129 / 2022
Annales Polonici Mathematici 129 (2022), 25-41
MSC: Primary 37F10; Secondary 30D30.
DOI: 10.4064/ap190820-31-3
Opublikowany online: 20 June 2022
Streszczenie
We consider the class 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.
