{"paper":{"title":"Some universality results for dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"\\'Etienne Matheron, Udayan B. Darji","submitted_at":"2015-12-03T22:13:08Z","abstract_excerpt":"We prove some \"universality\" results for topological dynamical systems. In particular, we show that for any continuous self-map $T$ of a perfect Polish space, one can find a dense, $T$-invariant set homeomorphic to the Baire space ${\\mathbb N}^{\\mathbb N}$; that there exists a bounded linear operator $U: \\ell_1 \\rightarrow \\ell_1$ such that any linear operator $T$ from a separable Banach space into itself with $\\Vert T\\Vert\\leq 1$ is a linear factor of $U$; and that given any $\\sigma$-compact family ${\\mathcal F}$ of continuous self-maps of a compact metric space, there is a continuous self-ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01266","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":""},"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"}