{"paper":{"title":"Applied Koopmanism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP","nlin.CD"],"primary_cat":"math.DS","authors_text":"Igor Mezi\\'c, Marko Budi\\v{s}i\\'c, Ryan M. Mohr","submitted_at":"2012-06-14T16:19:52Z","abstract_excerpt":"A majority of methods from dynamical systems analysis, especially those in applied settings, rely on Poincar\\'e's geometric picture that focuses on \"dynamics of states\". While this picture has fueled our field for a century, it has shown difficulties in handling high-dimensional, ill-described, and uncertain systems, which are more and more common in engineered systems design and analysis of \"big data\" measurements.\n  This overview article presents an alternative framework for dynamical systems, based on the \"dynamics of observables\" picture. The central object is the Koopman operator: an infi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3164","kind":"arxiv","version":3},"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"}