We show a Wolff–Denjoy type theorem in complete geodesic spaces in the spirit of Beardon's framework that unifies several results in this area. In particular, it applies to strictly convex bounded domains in ${\mathbb{R}}^n$ or ${\mathbb{C}}^n$ with respect to a large class of metrics including Hilbert's and Kobayashi's metrics. The results are generalized to 1-Lipschitz compact mappings in infinite-dimensional Banach spaces.

中文翻译：

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测地线空间中的 Wolff–Denjoy 定理

我们本着 Beardon 框架的精神在完整的测地线空间中展示了 Wolff-Denjoy 类型定理，该框架统一了该领域的几个结果。特别是，它适用于严格凸有界域${\mathbb{电阻}}^n$ 或 ${\mathbb{丙}}^n$关于一大类指标，包括希尔伯特和小林的指标。结果被推广到无限维 Banach 空间中的 1-Lipschitz 紧致映射。