论文标题
逃脱通勤函数的点数有限多极。
Escaping points of commuting meromorphic functions with finitely many poles
论文作者
论文摘要
令$ f $和$ g $是通勤的，具有有限多极的杂种功能。通过研究该通勤关系下的FATOU组件的行为，我们证明$ f $和$ g $在$ f $和$ g $的情况下都具有相同的朱莉娅套装，没有简单地连接快速移动的徘徊域。通过将其与Tsantaris的最新结果相结合，我们获得了有关通勤函数的朱莉娅集合的最强烈的陈述（迄今为止）。为了强调整个情况的差异，我们表明具有有限多极的轨道具有轨道的先验性异常函数在接近极点和以惊人的快速速度逃到无穷大之间的轨道。
Let $f$ and $g$ be commuting meromorphic functions with finitely many poles. By studying the behaviour of Fatou components under this commuting relation, we prove that $f$ and $g$ have the same Julia set whenever $f$ and $g$ have no simply connected fast-escaping wandering domains. By combining this with a recent result of Tsantaris', we obtain the strongest statement (to date) regarding the Julia sets of commuting meromorphic functions. In order to highlight the difference to the entire case, we show that transcendental meromorphic functions with finitely many poles have orbits that alternate between approaching a pole and escaping to infinity at strikingly fast rates.
