{"paper":{"title":"On the continuity of global attractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Eric J. Olson, James C. Robinson, Luan Hoang","submitted_at":"2014-07-11T21:29:48Z","abstract_excerpt":"Let $\\Lambda$ be a complete metric space, and let $\\{S_\\lambda(\\cdot):\\ \\lambda\\in\\Lambda\\}$ be a parametrised family of semigroups with global attractors ${\\mathscr A}_\\lambda$. We assume that there exists a fixed bounded set $D$ such that ${\\mathscr A}_\\lambda\\subset D$ for every $\\lambda\\in\\Lambda$. By viewing the attractors as the limit as $t\\to\\infty$ of the sets $S_\\lambda(t)D$, we give simple proofs of the equivalence of `equi-attraction' to continuity (when this convergence is uniform in $\\lambda$) and show that the attractors ${\\mathscr A}_\\lambda$ are continuous in $\\lambda$ at a res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3306","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"}