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

Abstract

We consider two families of functions $\mathcal{F}=\{f_{{\la},ξ}(z)= e^{-z+\la}+ξ: \la,\,ξ\in\C, \RE{\la}<0, \REξ\geq 1\}$ and $\mathcal{F}'=\{f_{μ,{\ze}}(z)= e^{z+μ}+\ze: μ,\,\ze\in\C, \REμ<0, \RE\ze\leq-1\}$ 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.

8 pages. Accepted in Math Student. arXiv admin note: text overlap with arXiv:1401.0425