{"paper":{"title":"Fixed points for nilpotent actions on the plane and the Cartwright-Littlewood theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"J. Rib\\'on, J. Velasco, S. Firmo","submitted_at":"2013-06-02T17:46:51Z","abstract_excerpt":"The goal of this paper is proving the existence and then localizing global fixed points for nilpotent groups generated by homeomorphisms of the plane satisfying a certain Lipschitz condition. The condition is inspired in a classical result of Bonatti for commuting diffeomorphisms of the 2-sphere and in particular it is satisfied by diffeomorphisms, not necessarily of class $C^{1}$, whose linear part at every point is uniformly close to the identity. In this same setting we prove a version of the Cartwright-Littlewood theorem, obtaining fixed points in any continuum preserved by a nilpotent act"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0232","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"}