{"paper":{"title":"Horseshoes and Lyapunov exponents for Banach cocycles over nonuniformly hyperbolic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Rui Zou, Yongluo Cao","submitted_at":"2019-02-15T11:04:13Z","abstract_excerpt":"Let $f$ be a $C^r$$(r>1)$ diffeomorphism of a compact Riemannian manifold $M$, preserving an ergodic hyperbolic measure $\\mu$ with positive entropy, and let $\\mathcal{A}$ be a H\\\"older continuous cocycle of injective bounded linear operators acting on a Banach space $X$. We prove that there is a sequence of horseshoes for $f$ and dominated splittings for $\\mathcal{A}$ on the horseshoes, such that not only the measure theoretic entropy of $f$ but also the Lyapunov exponents of $\\mathcal{A}$ with respect to $\\mu$ can be approximated by the topological entropy of $f$ and the Lyapunov exponents of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05768","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"}