{"paper":{"title":"Continuity of Hausdorff dimension across generic dynamical Lagrange and Markov spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aline Cerqueira, Carlos Gustavo Moreira, Carlos Matheus","submitted_at":"2016-02-15T12:26:07Z","abstract_excerpt":"Let $\\varphi_0$ be a smooth area-preserving diffeomorphism of a compact surface $M$ and let $\\Lambda_0$ be a horseshoe of $\\varphi_0$ with Hausdorff dimension strictly smaller than one. Given a smooth function $f:M\\to \\mathbb{R}$ and a small smooth area-preserving perturtabion $\\varphi$ of $\\varphi_0$, let $L_{\\varphi, f}$, resp. $M_{\\varphi, f}$ be the Lagrange, resp. Markov spectrum of asymptotic highest, resp. highest values of $f$ along the $\\varphi$-orbits of points in the horseshoe $\\Lambda$ obtained by hyperbolic continuation of $\\Lambda_0$.\n  We show that, for generic choices of $\\varp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04649","kind":"arxiv","version":2},"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"}