Hilbert非扩张映射的动力学
Dynamics of Hilbert nonexpansive maps
摘要：
在他的工作的基础几何，希尔伯特指出，一个公式出现在工程贝尔特拉米，凯莱和克莱因，使一个完整的度量任何有界凸区域。几十年后，加勒特·伯克霍夫（Garrett Birkhoff）和汉斯·萨麦尔森（Hans Samelson）注意到，当考虑收缩该度量的某些凸锥映射时，该度量有有趣的应用。这种情况已经出现在许多情况下，纯粹的和应用，并可以被称为非线性Perron-Frobenius理论。本文围绕这一理论的一个动力学方面展开。
英文摘要：
In his work on the foundations of geometry, Hilbert observed that a formula which appeared in works by Beltrami, Cayley, and Klein, gives rise to a complete metric on any bounded convex domain. Some decades later, Garrett Birkhoff and Hans Samelson noted that this metric has interesting applications, when considering certain maps of convex cones that contract the metric. Such situations have since arisen in many contexts, pure and applied, and could be called nonlinear Perron-Frobenius theory. This note centers around one dynamical aspect of this theory.
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。
