{"paper":{"title":"On the thin boundary of the fat attractor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Elismar R. Oliveira","submitted_at":"2014-02-28T16:39:37Z","abstract_excerpt":"For, $0<\\lambda<1$, consider the transformation $T(x) = d x $ (mod 1) on the circle $S^1$, a $C^1$ function $A:S^1 \\to \\mathbb{R}$, and, the map $F(x,s) = ( T(x) , \\lambda \\, s + A(x))$, $(x,s)\\in S^1 \\times \\mathbb{R}$. We denote $\\mathcal{B}= \\mathcal{B}_\\lambda$ the upper boundary of the attractor (known as fat attractor). We are interested in the regularity of $\\mathcal{B}_\\lambda$, and, also in what happens in the limit when $\\lambda\\to 1$. We also address the analysis of the following conjecture which were proposed by R. Bam\\'on, J. Kiwi, J. Rivera-Letelier and R. Urz\\'ua: for any fixed "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.7313","kind":"arxiv","version":4},"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"}