{"paper":{"title":"Persistence of fixed points under rigid perturbations of maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Pedro A. S. Salom\\~ao, Salvador Addas-Zanata","submitted_at":"2014-04-04T16:26:21Z","abstract_excerpt":"Let $f:S^1\\times [0,1]\\to S^1\\times [0,1]$ be a real-analytic annulus diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift $\\tilde {f}:\\mathbb{R}\\times [0,1]\\rightarrow \\mathbb{R}\\times [0,1]$ we have ${\\rm Fix}(\\tilde{f})=\\mathbb{R}\\times \\{0\\}$ and that $\\tilde{f}$ positively translates points in $\\mathbb{R}\\times \\{1\\}$. Let $\\tilde{f}_\\epsilon $ be the perturbation of $\\tilde{f}$ by the rigid horizontal translation $(x,y)\\mapsto (x+\\epsilon,y)$. We show that for all $\\epsilon >0$ sufficiently small we have ${\\rm Fix} (\\tilde{f}_\\epsilo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1302","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"}