论文标题
几何有限的超越整个功能
Geometrically finite transcendental entire functions
论文作者
论文摘要
对于多项式，朱莉娅集合的局部连通性是一个备受瞩目且重要的特性。实际上，当本地连接的$ d \ geq 2 $的多项式的朱莉娅集合时，拓扑动态可以完全描述为一个更简单的系统的商：圆圈上的角度$ d $ -tupling。 对于整个函数，本地连接不太重要，但是我们仍可能要求将拓扑动态描述为简单系统的商。为此，我们介绍了“温顺”功能的概念：如果它是合适的分离型函数的商，则具有有限后集合的先验整个功能是条件。此外，我们证明了大类的几何有限的先验整个功能的能力，并在朱莉娅集合上具有界限。这可以看作是朱莉娅集合的局部连通性，用于几何有限多项式，首先是由杜阿迪和哈伯德证明的，并扩展了第二作者和Mihaljević的先前工作，以提供整个功能的更多限制性类别。
For polynomials, local connectivity of Julia sets is a much-studied and important property. Indeed, when the Julia set of a polynomial of degree $d\geq 2$ is locally connected, the topological dynamics can be completely described as a quotient of a much simpler system: angle $d$-tupling on the circle. For a transcendental entire function, local connectivity is less significant, but we may still ask for a description of the topological dynamics as the quotient of a simpler system. To this end, we introduce the notion of "docile" functions: a transcendental entire function with bounded postsingular set is docile if it is the quotient of a suitable disjoint-type function. Moreover, we prove docility for the large class of geometrically finite transcendental entire functions with bounded criticality on the Julia set. This can be seen as an analogue of the local connectivity of Julia sets for geometrically finite polynomials, first proved by Douady and Hubbard, and extends previous work of the second author and of Mihaljević for more restrictive classes of entire functions.
