We study the geometry of simply connected wandering domains for entire functions and we prove that every bounded connected regular open set, whose closure has a connected complement, is a wandering domain of some entire function. In particular such a domain can be realized as an escaping or an oscillating wandering domain. As a consequence, we obtain that every Jordan curve is the boundary of a wandering Fatou component of some entire function.

中文翻译：

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关于单连通游荡域的几何

我们研究了整个函数的简单连通游荡域的几何，我们证明了每个有界连通正则开集，其闭包具有连通补码，是某个完整函数的游荡域。特别地，这样的域可以实现为转义域或振荡漂移域。因此，我们得到每条Jordan曲线都是某个完整函数的一个漂移法头分量的边界。