{"paper":{"title":"Some ergodic properties of metrics on hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alex Furman, Uri Bader","submitted_at":"2017-07-07T02:20:27Z","abstract_excerpt":"Let $\\Gamma$ be a non-elementary Gromov-hyperbolic group, and $\\partial \\Gamma$ denote its Gromov boundary. We consider $\\Gamma$-invariant proper $\\delta$-hyperbolic, quasi-convex metric $d$ on $\\Gamma$, and the associated Patterson-Sullivan measure class $[\\nu]$ on $\\partial^{(2)}\\Gamma$, and its square $[\\nu\\times\\nu]$ on $\\partial^{(2)}\\Gamma$ -- the space of distinct pairs of points on the boundary. We construct an analogue of a geodesic flow to study ergodicity properties of the $\\Gamma$-actions on $(\\partial\\Gamma,\\nu)$ and on $(\\partial^{(2)}\\Gamma,[\\nu\\times\\nu])$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02020","kind":"arxiv","version":2},"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"}