3 papers
math.DS2026
Bounded-orbit wandering domains do not exist
Kostiantyn Drach, Leticia Pardo-Simón, Beno Učakar
This paper establishes that transcendental entire functions do not have wandering Fatou components whose forward orbit is bounded. This settles a long-standing question in transcen…
math.DS2026
On the geometry of unbounded wandering domains
Beno Učakar
We study the geometry of unbounded wandering domains of entire functions using Arakelian approximation. First, we show that, given a uniformly accessible closed set contained in a…
math.CV2025
Carleman approximation by non-critical functions on Riemann surfaces
Beno Učakar
We present the class of semi-admissible subsets of an open Riemann surface on which Carleman approximation by non-critical holomorphic functions is possible. In particular we chara…