{"paper":{"title":"Flexibility versus genericity of phase diagrams of perturbed continuous maps on the Cantor set","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hugo Marsan, Mathieu Sablik","submitted_at":"2025-08-01T09:33:38Z","abstract_excerpt":"Consider the dynamical system constitued by a continuous function $F:\\mathcal{A}^\\mathbb{N}\\to\\mathcal{A}^\\mathbb{N}$ where $\\mathcal{A}$ is a finite alphabet. The perturbed counterpart, denoted by $F_\\epsilon$, is obtained after each iteration of $F$ by modifying each cell independently with probability $\\epsilon\\in[0,1]$ and choosing the new value uniformly. We characterize the possible sets of $\\epsilon\\in[0,1]$ such that $F_\\epsilon$ has a unique measure. These sets are exactly the $G_\\delta$ sets (countable intersection of open sets) of $[0, 1]$ which contain 1. However, we show that gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00461","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/2508.00461/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"}