{"paper":{"title":"Concentration of dimension in the Lagrange spectrum","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Christian Camilo Silva Villamil","submitted_at":"2024-11-25T21:20:40Z","abstract_excerpt":"Let $\\varphi$ be a smooth conservative diffeomorphism of a compact surface $S$ and let $\\Lambda$ be a mixing horseshoe of $\\varphi$. Given a smooth real function $f$ defined on $S$, we define for points $\\eta$ in the unstable Cantor set of the pair $(\\varphi,\\Lambda)$, a generalization, $k_{\\varphi,\\Lambda,f}(\\eta)$, of the best constant of Diophantine approximation for irrational numbers. We study the set of points $\\eta$ for which the sets $k_{\\varphi,\\Lambda,f}^{-1}((-\\infty,\\eta])$ and $k_{\\varphi,\\Lambda,f}^{-1}(\\eta)$ have the same Hausdorff dimension and when the Hausdorff dimension of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16939","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.16939/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}