Wandering domains for entire functions of finite order in the Eremenko-Lyubich class
Wandering domains for entire functions of finite order in the Eremenko-Lyubich class
复制标题
Eremenko-Lyubich 类中有限阶整个函数的游走域
DOI：
10.1112/plms.12288
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发表时间：
2019
影响因子：
1.8
通讯作者：
Shishikura Mitsuhiro
中科院分区：
文献类型：
--
作者：
Marti‐Pete David;Shishikura Mitsuhiro
最近，Bishop使用一种称为拟共形折叠的新技术构造了第一个具有游荡域的有界型超越整函数的例子。很容易检查他的方法是否产生了一个无穷级的完整函数。我们在具有游荡域的类中构造了有限级整函数的第一个例子。与毕晓普的情况一样，这些游荡的区域是振荡型的，也就是说，它们有一个无界的不可逃逸的轨道。为了构造这样的函数，我们使用拟正则内插而不是拟共形折叠，这要简单得多。我们的例子对任何人都是有序的，因为类中函数的次序至少是有序的，所以我们得到了可能的最小次序。最后，我们可以修改结构以获得具有任意数目的游荡域的宏轨道的类中的有限级函数，包括无穷多个。
Recently, Bishop constructed the first example of a bounded‐type transcendental entire function with a wandering domain using a new technique called quasiconformal folding. It is easy to check that his method produces an entire function of infinite order. We construct the first examples of entire functions of finite order in classwith wandering domains. As in Bishop's case, these wandering domains are of oscillating type, that is, they have an unbounded non‐escaping orbit. To construct such functions we use quasiregular interpolation instead of quasiconformal folding, which is much more straightforward. Our examples have orderfor anyand, since the order of functions in classis at least, we achieve the smallest possible order. Finally, we can modify the construction to obtain functions of finite order in classwith any number of grand orbits of wandering domains, including infinitely many.