{"paper":{"title":"The approximation of Lyapunov exponents by horseshoes for $C^1$-diffeomorphisms with dominated splitting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Juan Wang, Rui Zou, Yongluo Cao","submitted_at":"2019-01-10T04:26:53Z","abstract_excerpt":"Let $f$ be a $C^1$-diffeomorphism and $\\mu$ be a hyperbolic ergodic $f$-invariant Borel probability measure with positive measure-theoretic entropy. Assume that the Oseledec splitting $$T_xM=E_1(x) \\oplus\\cdots\\oplus E_s(x) \\oplus E_{s+1}(x) \\oplus\\cdots\\oplus E_l(x) $$ is dominated on the Oseledec basin $\\Gamma$. We give extensions of Katok's Horseshoes construction. Moreover there is a dominated splitting corresponding to Oseledec subspace on horseshoes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03013","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"}