{"paper":{"title":"Topological dynamics for the endograph metric I: Equivalences with other metrics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Antoni L\\'opez-Mart\\'inez","submitted_at":"2025-10-20T18:10:55Z","abstract_excerpt":"Given a dynamical system $(X,f)$ we investigate several topological dynamical properties for its Zadeh extension $(\\mathcal{F}(X),\\hat{f})$ endowed with the endograph metric $d_{E}$. In particular, we prove that for topological $\\mathcal{A}$-transitivity, topological $(\\ell,\\mathcal{A})$-recurrence, Devaney chaos, and for the specification property, the endograph metric behaves similarly to the supremum metric $d_{\\infty}$, the Skorokhod metric $d_{0}$ and the sendograph metric $d_{S}$. Our results not only resolve certain open questions in the existing literature, but also yield completely ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.17990","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/2510.17990/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"}