{"paper":{"title":"On weak product recurrence and synchronization of return times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guo Hua Zhang, Piotr Oprocha","submitted_at":"2012-05-10T14:44:00Z","abstract_excerpt":"The paper is devoted to study of product recurrence. First, we prove that notions of $\\F_{ps}-PR$ and $\\F_{pubd}-PR$ are exactly the same as product recurrence, completing that way results of [P. Dong, S. Shao and X. Ye, \\emph{Product recurrent properties, disjointness and weak disjointness}, Israel J. Math.], and consequently, extending the characterization of return times of distal points which originated from works of Furstenberg. We also study the structure of the set of return times of weakly mixing sets. As a consequence, we obtain new sufficient conditions for $\\F_{s}-PR$ and also find "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2280","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"}