{"intvolume":"        24","language":[{"iso":"eng"}],"volume":24,"date_updated":"2021-01-12T08:20:34Z","type":"journal_article","extern":"1","publication":"Regular and Chaotic Dynamics","publication_status":"published","abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","doi":"10.1134/S1560354719060017","author":[{"first_name":"Luigi","full_name":"Chierchia, Luigi","last_name":"Chierchia"},{"last_name":"Koudjinan","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","full_name":"Koudjinan, Edmond","first_name":"Edmond","orcid":"0000-0003-2640-4049"}],"main_file_link":[{"url":"https://arxiv.org/abs/1908.02523","open_access":"1"}],"_id":"8693","title":"V. I. Arnold’s “pointwise” KAM theorem","quality_controlled":"1","citation":{"ieee":"L. Chierchia and E. Koudjinan, “V. I. Arnold’s ‘pointwise’ KAM theorem,” <i>Regular and Chaotic Dynamics</i>, vol. 24. Springer, pp. 583–606, 2019.","mla":"Chierchia, Luigi, and Edmond Koudjinan. “V. I. Arnold’s ‘Pointwise’ KAM Theorem.” <i>Regular and Chaotic Dynamics</i>, vol. 24, Springer, 2019, pp. 583–606, doi:<a href=\"https://doi.org/10.1134/S1560354719060017\">10.1134/S1560354719060017</a>.","ama":"Chierchia L, Koudjinan E. V. I. Arnold’s “pointwise” KAM theorem. <i>Regular and Chaotic Dynamics</i>. 2019;24:583–606. doi:<a href=\"https://doi.org/10.1134/S1560354719060017\">10.1134/S1560354719060017</a>","short":"L. Chierchia, E. Koudjinan, Regular and Chaotic Dynamics 24 (2019) 583–606.","apa":"Chierchia, L., &#38; Koudjinan, E. (2019). V. I. Arnold’s “pointwise” KAM theorem. <i>Regular and Chaotic Dynamics</i>. Springer. <a href=\"https://doi.org/10.1134/S1560354719060017\">https://doi.org/10.1134/S1560354719060017</a>","chicago":"Chierchia, Luigi, and Edmond Koudjinan. “V. I. Arnold’s ‘Pointwise’ KAM Theorem.” <i>Regular and Chaotic Dynamics</i>. Springer, 2019. <a href=\"https://doi.org/10.1134/S1560354719060017\">https://doi.org/10.1134/S1560354719060017</a>.","ista":"Chierchia L, Koudjinan E. 2019. V. I. Arnold’s “pointwise” KAM theorem. Regular and Chaotic Dynamics. 24, 583–606."},"date_created":"2020-10-21T15:25:45Z","month":"12","article_processing_charge":"No","date_published":"2019-12-10T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"page":"583–606","year":"2019","status":"public","article_type":"original","publisher":"Springer","external_id":{"arxiv":["1908.02523"]},"day":"10"}