{"paper":{"title":"Hopf-Tsuji-Sullivan dichotomy for quotients of Hadamard spaces with a rank one isometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Gabriele Link","submitted_at":"2017-06-01T17:25:57Z","abstract_excerpt":"Let $X$ be a proper Hadamard space and $\\Gamma< Isom(X)$ 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 of $X$ by $\\Gamma$ and with respect to Ricks' measure introduced in [MR3628926]. 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00402","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}