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Generic measures for hyperbolic flows on non-compact spaces

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Abstract

We consider the geodesic flow on a complete connected negatively curved manifold. We show that the set of invariant borel probability measures contains a dense G δ -subset consisting of ergodic measures fully supported on the non-wandering set. We also treat the case of non-positively curved manifolds and provide general tools to deal with hyperbolic systems defined on non-compact spaces.

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Authors and Affiliations

  1. IRMAR, Université Rennes1, campus Beaulieu, bât.23 35042, Rennes cedex, France

    Yves Coudene

  2. LAMFA, Université Picardie Jules Verne, 33 rue St Leu, 80000, Amiens, France

    Barbara Schapira

Authors
  1. Yves Coudene
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  2. Barbara Schapira
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Correspondence to Yves Coudene.

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Coudene, Y., Schapira, B. Generic measures for hyperbolic flows on non-compact spaces. Isr. J. Math. 179, 157–172 (2010). https://doi.org/10.1007/s11856-010-0076-z

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  • DOI: https://doi.org/10.1007/s11856-010-0076-z

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