{"paper":{"title":"Gibbs measures for foliated bundles with negatively curved leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"S\\'ebastien Alvarez","submitted_at":"2013-11-14T16:48:24Z","abstract_excerpt":"In this paper we develop a notion of Gibbs measure for the geodesic flow tangent to a foliated bundle over a compact and negatively curved basis. We also develop a notion of $F$-harmonic measure and prove that there exists a natural bijective correspondence between the two.\n  For projective foliated bundles with $\\mathbb{C}\\mathbb{P}^1$-fibers without transverse invariant measure, we show the uniqueness of these measures for any H\\\"older potential on the basis. In that case we also prove that $F$-harmonic measures are realized as weighted limits of large balls tangent to the leaves and that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3574","kind":"arxiv","version":3},"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"}