2020/10/19 by Leticia Pardo-Simón, Pardo-Simón, Leticia · 1 citation
Mathematics · #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS
paper · pdf · doi:10.48550/arxiv.2010.09845
V2: Author accepted manuscript. To appear in Discrete Contin. Dyn. Syst
arxiv created 2021/08/17 · arxiv updated 2021/08/18
It is known that, for many transcendental entire functions in the Eremenko-Lyubich class B, every escaping point can eventually be connected to infinity by a curve of escaping points. When this is the case, we say that the functions are criniferous. In this paper, we extend this result to a new class of maps in B. Furthermore, we show that if a map belongs to this class, then its Julia set contains a Cantor bouquet; in other words, it is a subset of ℂ ambiently homeomorphic to a straight brush.