{"paper":{"title":"On cusps and flat tops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Neil Dobbs","submitted_at":"2008-01-24T18:39:43Z","abstract_excerpt":"We develop non-invertible Pesin theory for a new class of maps called cusp maps. These maps may have unbounded derivative, but nevertheless verify a property analogous to $C^{1+\\epsilon}$. We do not require the critical points to verify a non-flatness condition, so the results are applicable to $C^{1+\\epsilon}$ maps with flat critical points. If the critical points are too flat, then no absolutely continuous invariant probability measure can exist. This generalises a result of Benedicks and Misiurewicz."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3815","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"}