BOUNDARIES OF ESCAPING FATOU COMPONENTS

作者：Rippon P J^*; Stallard G M

来源：Proceedings of the American Mathematical Society, 2011, 139(8): 2807-2820.

DOI：10.1090/S0002-9939-2011-10842-6

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) boolean OR {infinity} is connected.

• 出版日期2011-8