{"paper":{"title":"Pluripotency of wandering dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Shin Kiriki, Teruhiko Soma, Yushi Nakano","submitted_at":"2024-03-30T12:11:37Z","abstract_excerpt":"This paper isolates a perturbative mechanism, which we call \\emph{pluripotency}, by which the symbolic and statistical behavior of prescribed orbits in a uniformly hyperbolic set can be realized, after an arbitrarily small perturbation, along the forward orbits of all points in a set of positive Lebesgue measure.\n  In this sense, pluripotency provides a way of reprogramming dynamics from both statistical and geometric viewpoints: the empirical measures of all points in a positive-measure set can be made to asymptotically follow those of a prescribed orbit in the hyperbolic set. We first give a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.00337","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.00337/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"}