{"paper":{"title":"Generating positive geometric entropy from recurrent leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gabriel Ponce","submitted_at":"2016-08-12T23:55:19Z","abstract_excerpt":"In this paper we introduce a new $C^r-$perturbation procedure, with respect to the $C^r$-Epstein topology, for $C^r$-foliations by surfaces. Using this perturbation procedure we show how one can use the existence of recurrent leaves of certain $C^r-$foliation $\\mathcal F$ to obtain a foliation $\\mathcal G$, $C^r-$close to $\\mathcal F$ in the $C^r-$Epstein topology, which has a resilient leaf. In particular, one can take advantage of recurrence property to construct examples of $C^r-$foliations by surfaces, $C^r-$close to each other and such that one of them has a resilient leaf while the other"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03925","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"}