{"paper":{"title":"On a generalization of the Cartwright-Littlewood fixed point theorem for planar homeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jan P. Boro\\'nski","submitted_at":"2015-10-22T15:54:11Z","abstract_excerpt":"We prove a generalization of the fixed point theorem of Cartwright and Littlewood. Namely, suppose $h : \\mathbb{R}^2 \\to\\mathbb{R}^2$ is an orientation preserving planar homeomorphism, and let $C$ be a continuum such that $h^{-1}(C)\\cup C$ is acyclic. If there is a $c\\in C$ such that $\\{h^{-i}(c):i\\in\\mathbb{N}\\}\\subseteq C$, or $\\{h^i(c):i\\in\\mathbb{N}\\}\\subseteq C$, then $C$ also contains a fixed point of $h$. Our approach is based on Morton Brown's short proof of the result of Cartwright and Littlewood. In addition, making use of a linked periodic orbits theorem of Bonino we also prove a co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06663","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"}