A maximin characterization of the escape rate of nonexpansive mappings in metrically convex spaces
| Autor: | Gaubert, Stephane, Vigeral, Guillaume |
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| Rok vydání: | 2010 |
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| Zdroj: | Math. Proc. of Cambridge Phil. Soc., volume 152, pp. 341--363, 2012 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/S0305004111000673 |
| Popis: | We establish a maximin characterisation of the linear escape rate of the orbits of a non-expansive mapping on a complete (hemi-)metric space, under a mild form of Busemann's non-positive curvature condition (we require a distinguished family of geodesics with a common origin to satisfy a convexity inequality). This characterisation, which involves horofunctions, generalises the Collatz-Wielandt characterisation of the spectral radius of a non-negative matrix. It yields as corollaries a theorem of Kohlberg and Neyman (1981), concerning non-expansive maps in Banach spaces, a variant of a Denjoy-Wolff type theorem of Karlsson (2001), together with a refinement of a theorem of Gunawardena and Walsh (2003), concerning order-preserving positively homogeneous self-maps of symmetric cones. An application to zero-sum stochastic games is also given. Comment: 26 pages, 1 figure; v3: final version To appear in "Mathematical Proceedings of the Cambridge Philosophical Society" |
| Databáze: | arXiv |
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