{"slug":"paper-kolmogorov-a-n-1954-on-the-conservation-of-conditionally-periodic-motions-for-a","verification":{"valid":true,"entries":2,"head":"28477aed74ea50fa4daa531c4449fc399182fc1c5e60423ed8c084f49c0edd5d"},"count":2,"sources":[{"id":"s1","type":"other","url":"https://courses.seas.harvard.edu/climate/eli/Courses/APM203/2003fall/Kolmogorov-KAM-1954.pdf","title":"Kolmogorov A.N. On the conservation of conditionally periodic motions for a small change in Hamilton's function. Dokl. Akad. Nauk SSSR 98 (1954) 527-530. English translation LA-TR-71-67.","quote":"an s-parametric family of conditionally periodic motions persists under small change in the Hamilton function","summary":"Original note establishing persistence of quasi-periodic tori.","claim_ids":["c1","c2","c3"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-10T09:43:47.571Z","link_status":"ok","quote_status":"unverified","prev":"genesis","hash":"b7e2f1218be444b8f8c55cb66772f4c4bdd480a5d73731cc404efd352c8051b3"},{"id":"s2","type":"review","url":"https://arxiv.org/html/2402.00178v1","title":"Kolmogorov's new 'metrical approach' to Hamiltonian systems","quote":"We review Kolmogorov's 1954 fundamental paper","summary":"Review confirming analyticity requirement and later extensions by Arnold and Moser.","claim_ids":["c4"],"found_by":"grok/grok-4.3","extra":{},"accessed_at":"2026-07-10T09:43:47.571Z","link_status":"ok","quote_status":"unverified","prev":"b7e2f1218be444b8f8c55cb66772f4c4bdd480a5d73731cc404efd352c8051b3","hash":"28477aed74ea50fa4daa531c4449fc399182fc1c5e60423ed8c084f49c0edd5d"}]}