Non-expanding maps and Busemann functions
Non-expanding maps and Busemann functions
复制标题
非扩展映射和 Busemann 函数
DOI：
10.1017/s0143385701001699
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发表时间：
2001
影响因子：
0.9
通讯作者：
A. Karlsson
中科院分区：
文献类型：
--
作者：
A. Karlsson
本文对Beardon，[Be 1]和[Be 2]的一些结果给出了更强的版本和替代的简单证明.这些结果涉及局部紧度量空间的压缩，推广了Wolff和Denjoy关于单位圆盘上全纯映射迭代的定理。在无界轨道的情况下，有时可以证明两种类型的陈述;第一，关于不变的horoball，第二，关于迭代收敛到边界上的一点。类似类型的一些进一步的意见作出某些随机产品的反牵引和也有关反牵引的Gromov双曲空间。
We give stronger versions and alternative simple proofs of some results of Beardon, [Be1] and [Be2]. These results concern contractions of locally compact metric spaces and generalize the theorems of Wolff and Denjoy about the iteration of a holomorphic map of the unit disk. In the case of unbounded orbits, there are two types of statements which can sometimes be proven; first, about invariant horoballs, and second, about the convergence of the iterates to a point on the boundary. A few further remarks of similar type are made concerning certain random products of semicontractions and also concerning semicontractions of Gromov hyperbolic spaces.