Let f be a real entire function whose set S(f) of singular values is real andbounded. We show that, if f satisfies a certain function-theoretic condition(the "sector condition"), then $f$ has no wandering domains. Our resultincludes all maps of the form f(z)=\lambda sinh(z)/z + a, where a is a realconstant and {\lambda} is positive. We also show the absence of wandering domains for certain non-real entirefunctions for which S(f) is bounded and the iterates of f tend to infinityuniformly on S(f). As a special case of our theorem, we give a short, elementary andnon-technical proof that the Julia set of the complex exponential map f(z)=e^zis the entire complex plane. Furthermore, we apply similar methods to extend a result of Bergweiler,concerning Baker domains of entire functions and their relation to thepostsingular set, to the case of meromorphic functions.
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机译：令f是一个真实的完整函数，其奇异值的集合S（f）是有界的。我们证明，如果f满足特定的函数理论条件（“部门条件”），则$ f $没有漫游域。我们的结果包括形式为f（z）= \ lambda sinh（z）/ z + a的所有映射，其中a是实常数，而{\ lambda}是正数。我们还显示出对于S（f）有界且f的迭代项趋向于在S（f）上无限无限均匀地存在的某些非真实整函数，没有游荡域。作为我们定理的一个特例，我们给出了简短的，基本的和非技术性的证明，即复指数映射f（z）= e ^ zi的Julia集构成了整个复平面。此外，对于亚纯函数，我们应用相似的方法来扩展关于整个函数的Baker域及其与奇异集的关系的Bergweiler结果。
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