Boundaries of escaping Fatou components

Details Boundaries of escaping Fatou components Boundaries of escaping Fatou components

2010-09-22

arxiv.org/abs/1009.4450v1

Mathematics

Complex Variables

Scientific paper

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 $I(f)\cup\{\infty\}$ is connected.

Affiliated with

Also associated with

No associations

Rating

Boundaries of escaping Fatou components does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Boundaries of escaping Fatou components, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Boundaries of escaping Fatou components will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-638506