复双圆盘动力学
Dynamics in the complex bidisc
摘要：
设Delta^{n}是C^{n}中的单位多圆盘，f是Delta^{n}的全纯自映射.当n=1时，由Schwarz引理可知，f在单位圆内至多有一个不动点。如果不存在这样的点，那么f有一个唯一的边界点，称之为x，使得中心为x且半径R>0的每一个单圈E（x，R）都被f送入自身。这个边界点称为“f的Wolff点”。本文给出了定义在C^{n}的有界域上的全纯映射的Wolff点的定义。特别是我们的沃尔夫点，W（f），一个全纯自映射f的双圆盘的性质的组件的映射f本身的一组特征。
英文摘要：
Let Delta^{n} be the unit polydisc in C^{n} and let f be a holomorphic self map of Delta^{n}. When n=1, it is well known, by Schwarz's lemma, that f has at most one fixed point in the unit disc. If no such point exists then f has a unique boundary point, call it x, such that every horocycle E(x,R) of center x and radius R>0 is sent into itself by f. This boundary point is called the "Wolff point of f". In this paper we propose a definition of Wolff points for holomorphic maps defined on a bounded domain of C^{n}. In particular we characterize the set of Wolff points, W(f), of a holomorphic self-map f of the bidisc in terms of the properties of the components of the map f itself.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
