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arXiv · 1503.08077

On the set where the iterates of an entire function are neither escaping nor bounded

J. W. Osborne·D. J. Sixsmith
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Abstract

For a transcendental entire function f, we study the set of points BU(f) whose iterates under f neither escape to infinity nor are bounded. We give new results on the connectedness properties of this set and show that, if U is a Fatou component that meets BU(f), then most boundary points of U (in the sense of harmonic measure) lie in BU(f). We prove this using a new result concerning the set of limit points of the iterates of f on the boundary of a wandering domain. Finally, we give some examples to illustrate our results.

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BibTeXRIS

J. W. Osborne, D. J. Sixsmith. 2015-03-27. On the set where the iterates of an entire function are neither escaping nor bounded. https://doi.org/10.5186/aasfm.2016.4134

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