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arXiv · 1406.2453

On escaping sets of some families of entire functions and dynamics of composite entire functions

D. Kumar
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Abstract

We consider two families of functions $\mathcal{F}=\{f_{{\la},{\xi}}(z)= e^{-z+\la}+\xi: \la,\,\xi\in\C, \RE{\la}<0, \RE\xi\geq 1\}$ and $\mathcal{F}'=\{f_{{\mu},{\ze}}(z)= e^{z+\mu}+\ze: \mu,\,\ze\in\C, \RE{\mu}<0, \RE\ze\leq-1\}$ and investigate the escaping sets of members of the family $\mathcal F$ and $\mathcal F'.$ We also consider the dynamics of composite entire functions and provide conditions for equality of escaping sets of two transcendental entire functions.

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D. Kumar. 2014-06-10. On escaping sets of some families of entire functions and dynamics of composite entire functions. https://arxiv.org/abs/1406.2453

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