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October 2018 Area of the complement of the fast escaping sets of a family of entire functions
Song Zhang, Fei Yang
Kodai Math. J. 41(3): 531-553 (October 2018). DOI: 10.2996/kmj/1540951252

Abstract

Let $f$ be an entire function with the form $f(z)=P(e^z)/e^z$, where $P$ is a polynomial with $\deg(P)\geq2$ and $P(0)\neq 0$. We prove that the area of the complement of the fast escaping set (hence the Fatou set) of $f$ in a horizontal strip of width $2\pi$ is finite. In particular, the corresponding result can be applied to the sine family $\alpha\sin(z+\beta)$, where $\alpha\neq 0$ and $\beta\in\mathbf{C}$.

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Song Zhang. Fei Yang. "Area of the complement of the fast escaping sets of a family of entire functions." Kodai Math. J. 41 (3) 531 - 553, October 2018. https://doi.org/10.2996/kmj/1540951252

Information

Published: October 2018
First available in Project Euclid: 31 October 2018

zbMATH: 07000582
MathSciNet: MR3870702
Digital Object Identifier: 10.2996/kmj/1540951252

Rights: Copyright © 2018 Tokyo Institute of Technology, Department of Mathematics

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Vol.41 • No. 3 • October 2018
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