{"paper":{"title":"$C^1$ stability of endomorphisms on two dimensional manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. Portela, J. Iglesias","submitted_at":"2017-12-21T17:48:39Z","abstract_excerpt":"A set of necessary conditions for $C^1$ stability of noninvertible maps is presented. It is proved that the conditions are sufficient for $C^1$ stability in compact oriented manifolds of dimension two. An example given by F.Przytycki in 1977 is shown to satisfy these conditions. It is the first example known of a $C^1$ stable map (noninvertible and nonexpanding) in a manifold of dimension two, while a wide class of examples are already known in every other dimension. \\end{abstract}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08114","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"}