2010/09/22 by Philip J. Rippon, Rippon, Philip J., Gwyneth M. Stallard +1
Mathematics · #30D05 #37F10 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS #msc:30D05 #msc:37F10
paper · pdf · doi:10.48550/arxiv.1009.4450
arxiv created 2010/09/22 · arxiv updated 2010/09/23
Let f be a transcendental entire function and U be a Fatou component of f. We show that if U is an escaping wandering domain of f, then most boundary points of U (in the sense of harmonic measure) are also escaping. In the other direction we show that if enough boundary points of U are escaping, then U is an escaping Fatou component. Some applications of these results are given; for example, if I(f) is the escaping set of f, then I(f)∪\∞\ is connected.