{"paper":{"title":"Physical Measure and Absolute Continuity for One-Dimensional Center Direction","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Jiagang Yang, Marcelo Viana","submitted_at":"2010-12-02T17:28:51Z","abstract_excerpt":"For a class of partially hyperbolic $C^k$, $k>1$ diffeomorphisms with circle center leaves we prove existence and finiteness of physical (or Sinai-Ruelle-Bowen) measures, whose basins cover a full Lebesgue measure subset of the ambient manifold. Our conditions contain an open and dense subset of all $C^k$ partially hyperbolic skew-products on compact circle bundles.\n  Our arguments blend ideas from the theory of Gibbs states for diffeomorphisms with mostly contracting center direction together with recent progress in the theory of cocycles over hyperbolic systems that call into play geometric "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0513","kind":"arxiv","version":1},"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"}