Slow escape in tracts
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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.References
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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
- MR Author ID: 1255171
- Email: james.waterman@open.ac.uk
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3087-3101
- MSC (2010): Primary 37F10; Secondary 30D05
- DOI: https://doi.org/10.1090/proc/14509
- MathSciNet review: 3973909