Rempe, Lasse ORCID: 0000-0001-8032-8580
(2022)
ESCAPING SETS ARE NOT SIGMA-COMPACT.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 150 (1).
pp. 171-177.
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Official URL: http://dx.doi.org/10.1090/proc/15576
Abstract
Let $f$ be a transcendental entire function. The escaping set $I(f)$ consists of those points that tend to infinity under iteration of $f$. We show that $I(f)$ is not $\sigma$-compact, resolving a question of Rippon from 2009.
Item Type: | Article |
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Additional Information: | 6 pages. To appear in Proc. Amer. Math. Soc. V4: Author accepted manuscript. Clarification of an imprecise statement regarding nowhere density in Corollary 2.2 that was present in v3 |
Uncontrolled Keywords: | math.DS, math.DS, math.CV, math.GN, Primary 30D05, Secondary 37F10, 54D45 |
Depositing User: | Symplectic Admin |
Date Deposited: | 16 Sep 2020 10:17 |
Last Modified: | 15 Mar 2024 05:05 |
DOI: | 10.1090/proc/15576 |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3101280 |
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