{"paper":{"title":"Any Baumslag-Solitar action on surfaces with a pseudo-Anosov element has a finite orbit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.DS","authors_text":"Isabelle Liousse, Nancy Guelman","submitted_at":"2017-03-27T12:41:45Z","abstract_excerpt":"We consider $f, h$ homeomorphims generating a faithful $BS(1,n)$-action on a closed surface $S$, that is, $h f h^{-1} = f^n$, for some $ n\\geq 2$. According to \\cite{GL}, after replacing $f$ by a suitable iterate if necessary, we can assume that there exists a minimal set $\\Lambda$ of the action, included in $Fix(f)$.\n  Here, we suppose that $f$ and $h$ are $C^1$ in neighbourhood of $\\Lambda$ and any point $x\\in\\Lambda$ admits an $h$-unstable manifold $W^u(x)$. Using Bonatti's techniques, we prove that either there exists an integer $N$ such that $W^u(x)$ is included in $Fix(f^N)$ or there is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09037","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"}