{"paper":{"title":"Koopman principle eigenfunctions and linearization of diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Igor Mezi\\'c, Ryan Mohr","submitted_at":"2016-11-03T22:25:08Z","abstract_excerpt":"This paper considers a nonlinear dynamical system on a complex, finite dimensional Banach space which has an asymptotically stable, hyperbolic fixed point. We investigate the connection between the so-called principle eigenfunctions of the Koopman operator and the existence of a topological conjugacy between the nonlinear dynamics and its linearization in the neighborhood of the fixed point. The principle eigenfunctions generate an algebra of observables for the linear dynamics --- called the principle algebra --- which can be used to generate a sequence of approximate conjugacy maps in the sa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01209","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"}