Given two permutable entire functions f and g, we establish vital relationship between escaping sets of entire functions f, g and their composition. We provide some families of transcendental entire functions for which Eremenko’s conjecture holds. In addition, we investigate the dynamical properties of the mapping \(f(z)=z+1+e^{-z}.\)

中文翻译：

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整个函数及其组合的转义结果

给定两个可置换的完整函数f和g，我们在整个函数f、  g 的转义集及其组合之间建立了重要的关系。我们提供了一些 Eremenko 猜想成立的先验全函数族。此外，我们研究了映射的动力学性质\(f(z)=z+1+e^{-z}.\)