A maximin characterization of the escape rate of nonexpansive mappings in metrically convex spaces
| العنوان: | A maximin characterization of the escape rate of nonexpansive mappings in metrically convex spaces |
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| المؤلفون: | Guillaume Vigeral, Stéphane Gaubert |
| المساهمون: | Max-plus algebras and mathematics of decision (MAXPLUS), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS) |
| المصدر: | Mathematical Proceedings Mathematical Proceedings, Cambridge University Press (CUP), 2012, 152 (2), pp.341-363. ⟨10.1017/S0305004111000673⟩ Mathematical Proceedings of the Cambridge Philosophical Society Mathematical Proceedings of the Cambridge Philosophical Society, 2012, 152 (2), pp.341-363. ⟨10.1017/S0305004111000673⟩ |
| سنة النشر: | 2010 |
| مصطلحات موضوعية: | Pure mathematics, Geodesic, Spectral radius, General Mathematics, 010102 general mathematics, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Banach space, Metric Geometry (math.MG), Dynamical Systems (math.DS), 47H09, 15A48, Type (model theory), 16. Peace & justice, Curvature, 01 natural sciences, Convexity, 010101 applied mathematics, Matrix (mathematics), Metric space, Mathematics - Metric Geometry, FOS: Mathematics, 0101 mathematics, Mathematics - Dynamical Systems, [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG], Mathematics |
| الوصف: | 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. 26 pages, 1 figure; v3: final version To appear in "Mathematical Proceedings of the Cambridge Philosophical Society" |
| اللغة: | English |
| تدمد: | 0305-0041 1469-8064 |
| DOI: | 10.1017/S0305004111000673⟩ |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::978a5c115e0bed2a6a8128fbe08aaf42 http://arxiv.org/abs/1012.4765 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....978a5c115e0bed2a6a8128fbe08aaf42 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 03050041 14698064 |
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| DOI: | 10.1017/S0305004111000673⟩ |