Boundaries of Escaping Fatou Components
نویسنده
چکیده
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.
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