{"paper":{"title":"Asymmetric dynamics of outer automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mark C. Bell","submitted_at":"2016-08-04T14:34:22Z","abstract_excerpt":"We consider the action of an irreducible outer automorphism $\\phi$ on the closure of Culler--Vogtmann Outer space. This action has north-south dynamics and so, under iteration, points converge exponentially to $[T^\\phi_+]$.\n  For each $N \\geq 3$, we give a family of outer automorphisms $\\phi_k \\in \\textrm{Out}(\\mathbb{F}_N)$ such that as, $k$ goes to infinity, the rate of convergence of $\\phi_k$ goes to infinity while the rate of convergence of $\\phi_k^{-1}$ goes to one. Even if we only require the rate of convergence of $\\phi_k$ to remain bounded away from one, no such family can be construct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01550","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"}