{"paper":{"title":"Topologically Anosov plane homeomorphisms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gonzalo Cousillas, Jorge Groisman, Juliana Xavier","submitted_at":"2018-05-07T20:38:24Z","abstract_excerpt":"This paper deals with classifying the dynamics of {\\it Topologically Anosov} plane homeomorphisms. We prove that a Topologically Anosov homeomorphism $f:\\mathbb{R}^2 \\to \\mathbb{R}^2$ is conjugate to a homothety if it is the time one map of a flow. We also obtain results for the cases when the nonwandering set of $f$ reduces to a fixed point, or if there exists an open, connected, simply connected proper subset $U$ such that $U \\subset \\mathrm{Int}(\\overline {f(U)})$, and such that $ \\cup_{n\\geq 0} f^n (U)= \\mathbb{R}^2$. In the general case, we prove a structure theorem for the $\\alpha$-limit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02737","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"}