关于有限型整函数的阶不变性和面积性质
On invariance of order and the area property for finite-type entire functions
摘要：
设f是一个整函数，它只有1/2个临界值和渐近值。直到拓扑等价，函数$f$由组合信息确定，更准确地说，由称为“线复合体”的无限图确定。在本文中，我们讨论了一个自然的问题，即整函数的增长阶是否由这种组合信息决定。搜索的条件，意味着一个积极的答案，这个问题导致我们的“面积属性”，这原来是有关的许多有趣的和重要的问题，共形动力学和函数论。这些包括一个猜想的Eremenko和Lyubich，可测动力学的整个功能，并推动二次微分。我们还讨论了证据表明，不变性的秩序和面积财产失败的一般。
英文摘要：
Let f be an entire function that has only finitely many critical and asymptotic values. Up to topological equivalence, the function $f$ is determined by combinatorial information, more precisely by an infinite graph known as a "line-complex". In this note, we discuss the natural question whether the order of growth of an entire function is determined by this combinatorial information. The search for conditions that imply a positive answer to this question leads us to the "area property", which turns out to be related to many interesting and important questions in conformal dynamics and function theory. These include a conjecture of Eremenko and Lyubich, the measurable dynamics of entire functions, and pushforwards of quadratic differentials. We also discuss evidence that invariance of order and the area property fail in general.
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