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