论文标题
全体形态序列，非自治动力系统和徘徊域的边界动力学
Boundary dynamics for holomorphic sequences, non-autonomous dynamical systems and wandering domains
论文作者
论文摘要
与Denjoy-Wolff定理有关的经典结果，与单位光盘的全体形态自形图迭代下的内部点和边界点轨道之间的关系。在这里，我们第一次在简单连接的域之间的holomorphic Maps的序列$（f_n）$的一般设置中解决了此类问题。我们表明，尽管可以将某些经典结果推广，但对域的几何形状具有有趣的依赖性，但可以采取更丰富的行为。即使在经典环境中，我们的一些结果也是新的。 我们的方法特别适用于非自治动力学系统时，当$（f_n）$是全体形态图的正向组成时，以及研究全体形态动力学中流浪域的研究。 这些证明使用了几何函数理论，测量理论和千古理论的技术，示例的构建涉及第二个Borel-cantelli引理的“弱独立性”版本，以及来自“缩小目标”的厄尔贡理论的概念。
There are many classical results, related to the Denjoy--Wolff Theorem, concerning the relationship between orbits of interior points and orbits of boundary points under iterates of holomorphic self-maps of the unit disc. Here, for the first time, we address such questions in the very general setting of sequences $(F_n)$ of holomorphic maps between simply connected domains. We show that, while some classical results can be generalised, with an interesting dependence on the geometry of the domains, a much richer variety of behaviours is possible. Some of our results are new even in the classical setting. Our methods apply in particular to non-autonomous dynamical systems, when $(F_n)$ are forward compositions of holomorphic maps, and to the study of wandering domains in holomorphic dynamics. The proofs use techniques from geometric function theory, measure theory and ergodic theory, and the construction of examples involves a `weak independence' version of the second Borel--Cantelli lemma and the concept from ergodic theory of `shrinking targets'.
