{"article_type":"original","doi":"10.1134/S1560354719060017","title":"V. I. Arnold’s “pointwise” KAM theorem","quality_controlled":"1","abstract":[{"lang":"eng","text":"We review V. I. Arnold’s 1963 celebrated paper [1] Proof of A. N. Kolmogorov’s Theorem on the Conservation of Conditionally Periodic Motions with a Small Variation in the Hamiltonian, and prove that, optimising Arnold’s scheme, one can get “sharp” asymptotic quantitative conditions (as ε → 0, ε being the strength of the perturbation). All constants involved are explicitly computed."}],"author":[{"last_name":"Chierchia","full_name":"Chierchia, Luigi","first_name":"Luigi"},{"orcid":"0000-0003-2640-4049","first_name":"Edmond","full_name":"Koudjinan, Edmond","last_name":"Koudjinan","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E"}],"day":"10","citation":{"ista":"Chierchia L, Koudjinan E. 2019. V. I. Arnold’s “pointwise” KAM theorem. Regular and Chaotic Dynamics. 24, 583–606.","short":"L. Chierchia, E. Koudjinan, Regular and Chaotic Dynamics 24 (2019) 583–606.","ieee":"L. Chierchia and E. Koudjinan, “V. I. Arnold’s ‘pointwise’ KAM theorem,” Regular and Chaotic Dynamics, vol. 24. Springer, pp. 583–606, 2019.","ama":"Chierchia L, Koudjinan E. V. I. Arnold’s “pointwise” KAM theorem. Regular and Chaotic Dynamics. 2019;24:583–606. doi:10.1134/S1560354719060017","mla":"Chierchia, Luigi, and Edmond Koudjinan. “V. I. Arnold’s ‘Pointwise’ KAM Theorem.” Regular and Chaotic Dynamics, vol. 24, Springer, 2019, pp. 583–606, doi:10.1134/S1560354719060017.","chicago":"Chierchia, Luigi, and Edmond Koudjinan. “V. I. Arnold’s ‘Pointwise’ KAM Theorem.” Regular and Chaotic Dynamics. Springer, 2019. https://doi.org/10.1134/S1560354719060017.","apa":"Chierchia, L., & Koudjinan, E. (2019). V. I. Arnold’s “pointwise” KAM theorem. Regular and Chaotic Dynamics. Springer. https://doi.org/10.1134/S1560354719060017"},"volume":24,"publisher":"Springer","date_created":"2020-10-21T15:25:45Z","intvolume":" 24","extern":"1","oa_version":"Preprint","publication":"Regular and Chaotic Dynamics","external_id":{"arxiv":["1908.02523"]},"oa":1,"date_published":"2019-12-10T00:00:00Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","main_file_link":[{"url":"https://arxiv.org/abs/1908.02523","open_access":"1"}],"_id":"8693","page":"583–606","publication_status":"published","year":"2019","language":[{"iso":"eng"}],"date_updated":"2021-01-12T08:20:34Z","month":"12","type":"journal_article"}