论文标题
整个地图的结合和临界值
Combinatorics of criniferous entire maps with escaping critical values
论文作者
论文摘要
如果最终可以通过逃避点的曲线将其逃逸集中的每个点最终连接到Infinity，则先验整个功能被称为Criniferic。许多具有有限单数的超越整个功能具有此属性，并且该类最近在复杂的动力学中引起了很多关注。在存在临界值的存在下，这些曲线在临界点（预映射）处断开或分裂。在本文中，我们开发了组合工具，使我们能够完整描述任何criniforicer功能的逃避集，而没有渐近值的朱莉娅集合。特别是，我们的描述准确反映了分裂现象。这种组合结构为进一步研究这类功能奠定了基础。例如，我们在[Arxiv：1905.03778]中使用这些结果，对一类超越整个地图的拓扑动态进行了第一个完整的描述，并具有无限的后集集。
A transcendental entire function is called criniferous if every point in its escaping set can eventually be connected to infinity by a curve of escaping points. Many transcendental entire functions with bounded singular set have this property, and this class has recently attracted much attention in complex dynamics. In the presence of escaping critical values, these curves break or split at (preimages of) critical points. In this paper, we develop combinatorial tools that allow us to provide a complete description of the escaping set of any criniferous function without asymptotic values on its Julia set. In particular, our description precisely reflects the splitting phenomenon. This combinatorial structure provides the foundation for further study of this class of functions. For example, we use these results in [arXiv:1905.03778] to give the first full description of the topological dynamics of a class of transcendental entire maps with unbounded postsingular set.
