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Slow escape in tracts


Author: James Waterman
Journal: Proc. Amer. Math. Soc. 147 (2019), 3087-3101
MSC (2010): Primary 37F10; Secondary 30D05
DOI: https://doi.org/10.1090/proc/14509
Published electronically: April 8, 2019
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Abstract: Let $ f$ be a transcendental entire function. By a result of Rippon and Stallard, there exist points whose orbit escapes arbitrarily slowly. By using a range of techniques to prove new covering results, we extend their theorem to prove the existence of points which escape arbitrarily slowly within logarithmic tracts and tracts with certain boundary properties. We then give examples to illustrate our results in a variety of tracts.


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Additional Information

James Waterman
Affiliation: School of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, United Kingdom
Email: james.waterman@open.ac.uk

DOI: https://doi.org/10.1090/proc/14509
Received by editor(s): September 4, 2018
Received by editor(s) in revised form: November 1, 2018
Published electronically: April 8, 2019
Communicated by: Filippo Bracci
Article copyright: © Copyright 2019 American Mathematical Society