A note on an ergodic theorem in weakly uniformly convex geodesic spaces

Karlsson and Margulis [A. Karlsson, G. Margulis, A multiplicative ergodic theorem and nonpositively curved spaces. Commun. Math. Phys. 208 (1999), 107-123] proved in the setting of uniformly convex geodesic spaces, which additionally satisfy a nonpositive curvature condition, an ergodic theorem that...

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Detalles Bibliográficos
Autores: Leustean, Laurentiu, Nicolae, Adriana
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2015
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/48123
Acceso en línea:http://hdl.handle.net/11441/48123
https://doi.org/10.1007/s00013-015-0825-7
Access Level:acceso abierto
Palabra clave:Ergodic theorem
Geodesic space
Weak uniform convexity
Busemann convexity
Descripción
Sumario:Karlsson and Margulis [A. Karlsson, G. Margulis, A multiplicative ergodic theorem and nonpositively curved spaces. Commun. Math. Phys. 208 (1999), 107-123] proved in the setting of uniformly convex geodesic spaces, which additionally satisfy a nonpositive curvature condition, an ergodic theorem that focuses on the asymptotic behavior of integrable cocycles of nonexpansive mappings over an ergodic measure-preserving transformation. In this note we show that this result holds true when assuming a weaker notion of uniform convexity.