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

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Abstract

Karlsson and Margulis (Commun. Math. Phys. 208:107–123, 1999) 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.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, P. O. Box 010014, Bucharest, Romania

    Laurenţiu Leuştean

  2. Simion Stoilow Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, 014700, Bucharest, Romania

    Laurenţiu Leuştean

  3. Department of Mathematics, Babeş-Bolyai University, Kogălniceanu 1, 400084, Cluj-Napoca, Romania

    Adriana Nicolae

  4. Research Group of the Project PD-3-0152, Simion Stoilow Institute of Mathematics of the Romanian Academy, P. O. Box 1-764, 014700, Bucharest, Romania

    Adriana Nicolae

Authors
  1. Laurenţiu Leuştean
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  2. Adriana Nicolae
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Correspondence to Laurenţiu Leuştean.

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Leuştean, L., Nicolae, A. A note on an ergodic theorem in weakly uniformly convex geodesic spaces. Arch. Math. 105, 467–477 (2015). https://doi.org/10.1007/s00013-015-0825-7

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  • DOI: https://doi.org/10.1007/s00013-015-0825-7

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