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arXiv · 1510.03628

Lebesgue measure of escaping sets of entire functions of completely regular growth

Walter Bergweiler·Igor Chyzhykov
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Abstract

We give conditions ensuring that the Julia set and the escaping set of an entire function of completely regular growth have positive Lebesgue measure. The essential hypotheses are that the indicator is positive except perhaps at isolated points and that most zeros are located in neighborhoods of finitely many rays. We apply the result to solutions of linear differential equations.

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Walter Bergweiler, Igor Chyzhykov. 2016-06-16. Lebesgue measure of escaping sets of entire functions of completely regular growth. https://doi.org/10.1112/jlms%2Fjdw051

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