论文标题
无限的快速逃避徘徊域
Unbounded fast escaping wandering domains
论文作者
论文摘要
我们将一种新的近似技术引入复杂动力学的上下文中，该技术使我们能够构建具有无限徘徊域的先验整个功能的示例。我们提供了整个功能的示例，其中包括一个无限的快速逃避徘徊域的轨道，回答了里彭和夫的长期问题。此外，这些示例涵盖了所有可能的类型的简单连接的流浪域，从收敛到边界方面。与贝克的猜想有关，尚不清楚秩序的功能少于一个人可能具有无限的徘徊域。对于任何大于$ 1/2 $且小于$ 1 $的订单，我们提供了无限徘徊域的此类订单的全部功能。
We introduce a new approximation technique into the context of complex dynamics that allows us to construct examples of transcendental entire functions with unbounded wandering domains. We provide examples of entire functions with an orbit of unbounded fast escaping wandering domains, answering a long-standing question of Rippon and Stallard. Moreover, these examples cover all possible types of simply connected wandering domains in terms of convergence to the boundary. In relation to a conjecture of Baker, it was unknown whether functions of order less than one could have unbounded wandering domains. For any given order greater than $1/2$ and smaller than $1$, we provide an entire function of such order with an unbounded wandering domain.
