{"paper":{"title":"Generalized Recurrence and the Nonwandering Set for Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jim Wiseman","submitted_at":"2016-07-12T18:57:39Z","abstract_excerpt":"For continuous maps of compact metric spaces $f:X\\to X$ and $g:Y\\to Y$ and for various notions of topological recurrence, we study the relationship between recurrence for $f$ and $g$ and recurrence for the product map $f\\times g:X\\times Y \\to X\\times Y$. For the generalized recurrent set $GR$, we see that $GR(f\\times g)=GR(f)\\times GR(g)$. For the nonwandering set $NW$, we see that $NW(f\\times g)\\subset NW(f)\\times NW(g)$ and give necessary and sufficient conditions on $f$ for equality for every $g$. We also consider product recurrence for the chain recurrent set, the strong chain recurrent se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03465","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"}