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Exponential polynomials with Fatou and non-escaping sets of finite Lebesgue measure
Published online by Cambridge University Press: 20 November 2020
Abstract
We give conditions ensuring that the Fatou set and the complement of the fast escaping set of an exponential polynomial f both have finite Lebesgue measure. Essentially, these conditions are designed such that
$|f(z)|\ge \exp (|z|^\alpha )$
for some
$\alpha>0$
and all z outside a set of finite Lebesgue measure.
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- Original Article
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- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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- © The Author(s), 2020. Published by Cambridge University Press