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Hopf-Tsuji-Sullivan dichotomy for quotients of Hadamard spaces with a rank one isometry

  • * Corresponding author: Gabriele Link

    * Corresponding author: Gabriele Link
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  • Let $X$ be a proper Hadamard space and $\Gamma <{\text{Is}}(X)$ a non-elementary discrete group of isometries with a rank one isometry. We discuss and prove Hopf-Tsuji-Sullivan dichotomy for the geodesic flow on the set of parametrized geodesics of the quotient $\Gamma \backslash X$ and with respect to Ricks' measure introduced in [35]. This generalizes previous work of the author and J. C. Picaud on Hopf-Tsuji-Sullivan dichotomy in the analogous manifold setting and with respect to Knieper's measure.

    Mathematics Subject Classification: Primary: 37D40, 20F67; Secondary: 37D25.

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