{"paper":{"title":"Superstable manifolds of invariant circles and co-dimension 1 Bottcher functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Roland K. W. Roeder, Scott R. Kaschner","submitted_at":"2012-08-15T01:51:13Z","abstract_excerpt":"We consider the situation of a dominant meromorphic self-map $f: X -rightarrow X$, where $X$ is a compact K\\\"ahler manifold of dimension $n > 1$. Suppose there is an embedded copy of $\\mathbb{P}^1$ that is invariant under $f$, with $f$ holomorphic and transversally superattracting with degree $a$ in some neighborhood. Suppose $f$ restricted to this line is given by $z\\mapsto z^b$, with resulting invariant circle $S$. We prove that if $a \\geq b$, then the local stable manifold $W^s_\\loc(S)$ is real analytic. In fact, we state and prove a suitable localized version that can be useful in wider co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3013","kind":"arxiv","version":2},"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"}