{"paper":{"title":"On weak mixing, minimality and weak disjointness of all iterates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dominik Kwietniak, Piotr Oprocha","submitted_at":"2010-09-13T00:31:55Z","abstract_excerpt":"The article addresses some open questions about the relations between the topological weak mixing property and the transitivity of the map $f\\times f^2 \\times...\\times f^m$, where $f\\colon X\\ra X$ is a topological dynamical system on a compact metric space. The theorem stating that a weakly mixing and strongly transitive system is $\\Delta$-transitive is extended to a non-invertible case with a simple proof. Two examples are constructed, answering the questions posed by Moothathu [Colloq. Math. 120 (2010), no. 1, 127--138]. The first one is a multi-transitive non weakly mixing system, and the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2277","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"}