{"paper":{"title":"Multi-parameter persistence in dynamical systems for maximizing effects of control inputs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Tomoo Yokoyama, Yusuke Imoto","submitted_at":"2026-06-04T01:52:24Z","abstract_excerpt":"We introduce a new topological method to naturally extend a partial function $h \\colon X \\rightharpoonup [-\\infty, \\infty]$ on a ``generalization'' of a metric space $X$ equipped with a dynamical system $f \\colon X \\rightharpoonup X$, to a function $h_f^{\\varepsilon\\text{-}\\ell^p} \\colon X \\to [-\\infty,\\infty]$ with parameters $\\varepsilon,p$, which allows us to apply existing topological data analysis techniques to functions defined on the whole space. Moreover, given a function $h$ that evaluates the ``quality'' of points within $\\mathop{\\mathrm{dom}}h$, using this extended function, one can"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05577","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/2606.05577/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"}