Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces
Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces
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DOI：
10.1007/s11854-018-0022-2
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发表时间：
2018-02-01
影响因子：
1
通讯作者：
Wortel, Marten
中科院分区：
文献类型：
--
作者：
Lemmens, Bas;Lins, Brian;Wortel, Marten
我们研究巴纳赫空间中正常封闭圆锥内部的定点自由映射的动力学，该空间相对于希尔伯特度量或汤普森度量是非膨胀的。我们建立了几个 Denjoy-Wolff 型定理，证实了 Karlsson 和 Nussbaum 对一类重要的非扩张映射的猜想。我们还扩展了 Gaubert 和 Vigeral 关于此类非扩张映射的线性逃逸率的结果，并将其纳入更广泛的视角。
We study the dynamics of fixed point free mappings on the interior of a normal, closed cone in a Banach space that are nonexpansive with respect to Hilbert's metric or Thompson's metric. We establish several Denjoy-Wolff type theorems which confirm conjectures by Karlsson and Nussbaum for an important class of nonexpansive mappings. We also extend and put into a broader perspective results by Gaubert and Vigeral concerning the linear escape rate of such nonexpansive mappings.