{"paper":{"title":"Symbolic dynamics for surface diffeomorphisms with positive topological entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Omri Sarig","submitted_at":"2011-05-09T12:08:17Z","abstract_excerpt":"Suppose f is a C^{1+\\epsilon} surface diffeomorphism with positive topological entropy. For every positive \\delta strictly smaller than the topological entropy of f we construct an invariant Borel set E such that (a) f|E has a countable Markov partition; and (b) E has full measure with respect to any ergodic invariant probability measure with entropy larger than \\delta. This allows us to prove the following conjecture of A. Katok: if f is C^\\infty with topological entropy h>0, and if P_n(f)=#{x:f^n(x)=x}, then limsup P_n(f)/exp(nh)>0."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1650","kind":"arxiv","version":3},"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"}