{"paper":{"title":"Continuous Transitive Maps on the Interval Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bau-Sen Du","submitted_at":"2017-01-10T13:53:14Z","abstract_excerpt":"In this note, continuous transitive maps $f$ on the interval $I$ are re-addressed, where $I$ denotes one of the intervals: $(-\\infty, \\infty)$, $(-\\infty, a]$, $[b, \\infty)$, $[a, b]$, where $a < b$ are real numbers. Such maps must have a fixed point, say $z$, in the interior of $I$. Some well-known properties of such maps are re-proved in a systematic way according to the following :\n  (1) $f$ moves some point $c \\ne z$ away from $z$, i.e., fo some point $c \\ne z$, we have $f(c) \\le c < z$ or $z < c \\le f(c)$;\n  (2) $f$ moves some point $\\hat c \\ne z$ towards but not \"over\" $z$, i.e., for som"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02589","kind":"arxiv","version":5},"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"}