{"paper":{"title":"Dominated Splitting and Pesin's Entropy Formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.ST","physics.data-an","stat.TH"],"primary_cat":"math.DS","authors_text":"Wenxiang Sun, Xueting Tian","submitted_at":"2010-04-20T13:17:33Z","abstract_excerpt":"Let $M$ be a compact manifold and $f:\\,M\\to M$ be a $C^1$ diffeomorphism on $M$. If $\\mu$ is an $f$-invariant probability measure which is absolutely continuous relative to Lebesgue measure and for $\\mu$ $a.\\,\\,e.\\,\\,x\\in M,$ there is a dominated splitting $T_{orb(x)}M=E\\oplus F$ on its orbit $orb(x)$, then we give an estimation through Lyapunov characteristic exponents from below in Pesin's entropy formula, i.e., the metric entropy $h_\\mu(f)$ satisfies $$h_{\\mu}(f)\\geq\\int \\chi(x)d\\mu,$$ where $\\chi(x)=\\sum_{i=1}^{dim\\,F(x)}\\lambda_i(x)$ and $\\lambda_1(x)\\geq\\lambda_2(x)\\geq...\\geq\\lambda_{di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3441","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"}