We show that there is a transcendental meromorphic function with an invariant Baker domain U such that every singular value of f is a super-attracting periodic point. This answers a question of Bergweiler from 1993. We also show that U can be chosen to contain arbitrarily large round annuli, centred at zero, of definite modulus. This answers a question of Mihaljević and the author from 2013, and complements recent work of Barański et al concerning this question.

中文翻译：

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奇异轨道和贝克域

我们表明，存在一个具有不变Baker域U的先验亚纯函数，使得f的每个奇异值都是一个超吸引周期点。这回答了1993年Bergweiler的问题。我们还表明，可以选择U包含任意大的以零为模数的以0为中心的大圆环。这回答了Mihaljević和2013年作者的问题，并补充了Barański等人有关此问题的最新工作。