{"paper":{"title":"On the Orbits of not Expansive Mappings in Metric Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MG"],"primary_cat":"math.CV","authors_text":"Sergio Venturini","submitted_at":"2013-04-03T17:34:28Z","abstract_excerpt":"Let $\\MSpace$ be a locally compact metric space and let $\\pMap:\\MSpace\\to\\MSpace$ be a not expansive map. We prove that for each $\\ppa_0\\in\\MSpace$ the sequence $\\ppa_0,\\pMap(\\ppa_0),\\pMap^2(\\ppa_0),\\ldots$ is either relatively compact in $\\MSpace$ or compactly divergent in $\\MSpace$. As applications we study the structure of the functions which are limits of the iterates of the map $\\pMap$ and we prove the analyticity of the set of $\\pMap$-recurrent points when $\\pMap:\\MSpace\\to\\MSpace$ is a holomorphic and $\\MSpace$ is a complex hyperbolic spaces in the sense of Kobayashi."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1023","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"}