{"paper":{"title":"Dynamics of homeomorphisms of regular curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Issam Naghmouchi","submitted_at":"2018-06-30T20:19:19Z","abstract_excerpt":"In this paper, we prove first that the space of minimal sets of any homeomorphisms $f:X\\to X$ of a regular curve $X$ is closed in the hyperspace $2^X$ of closed subsets of $X$ endowed with the Hausdorff metric, and the non-wandering set $\\Omega (f)$ is equal to the set of recurrent points of $f$. Second, we study the continuity of the map $\\omega_f:X\\to 2^X;x\\mapsto \\omega_f (x) $, we show for instance the equivalence between the continuity of $\\omega_f $ and the equality between the $\\omega$-limit set and the $\\alpha $-limit set of every point in $X $. Finally, we prove that there is only one"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00222","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"}