{"paper":{"title":"Dynamics of Irreducible Endomorphisms of $F_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Patrick Reynolds","submitted_at":"2010-08-21T19:31:27Z","abstract_excerpt":"We consider the class non-surjective irreducible endomorphisms of the free group $F_n$. We show that such an endomorphism $\\phi$ is topologically represented by a simplicial immersion $f:G \\rightarrow G$ of a marked graph $G$; along the way we classify the dynamics of $\\partial \\phi$ acting on $\\partial F_n$: there are at most $2n$ fixed points, all of which are attracting. After imposing a necessary additional hypothesis on $\\phi$, we consider the action of $\\phi$ on the closure $\\bar{CV}_n$ of the Culler-Vogtmann Outer space. We show that $\\phi$ acts on $\\bar{CV}_n$ with \"sink\" dynamics: the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3659","kind":"arxiv","version":3},"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"}