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