{"paper":{"title":"Renormalization of Unicritical Diffeomorphisms of the Disk","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Enrique Pujals, Jonguk Yang, Mikhail Lyubich, Sylvain Crovisier","submitted_at":"2024-01-24T16:15:09Z","abstract_excerpt":"We introduce a class of infinitely renormalizable, unicritical diffeomorphisms of the disk (with a non-degenerate \"critical point\"). In this class of dynamical systems, we show that under renormalization, maps eventually become H\\'enon-like, and then converge super-exponentially fast to the space of one-dimensional unimodal maps. We also completely characterize the local geometry of every stable and center manifolds that exist in these systems. The theory is based upon a quantitative reformulation of the Oseledets-Pesin theory yielding a unicritical structure of the maps in question comprising"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.13559","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.13559/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}