[{"keyword":["Nearly{integrable Hamiltonian systems","perturbation theory","KAM Theory","Arnold's scheme","Kolmogorov's set","primary invariant tori","Lagrangian tori","measure estimates","small divisors","integrability on nowhere dense sets","Diophantine frequencies."],"publisher":"Springer Nature","intvolume":"        26","article_processing_charge":"No","scopus_import":"1","department":[{"_id":"VaKa"}],"publication_status":"published","page":"61-88","day":"03","abstract":[{"text":"This paper continues the discussion started in [CK19] concerning Arnold's legacy on classical KAM theory and (some of) its modern developments. We prove a detailed and explicit `global' Arnold's KAM Theorem, which yields, in particular, the Whitney conjugacy of a non{degenerate, real{analytic, nearly-integrable Hamiltonian system to an integrable system on a closed, nowhere dense, positive measure subset of the phase space. Detailed measure estimates on the Kolmogorov's set are provided in the case the phase space is: (A) a uniform neighbourhood of an arbitrary (bounded) set times the d-torus and (B) a domain with C2 boundary times the d-torus. All constants are explicitly given.","lang":"eng"}],"citation":{"ieee":"L. Chierchia and E. Koudjinan, “V.I. Arnold’s ‘“Global”’ KAM theorem and geometric measure estimates,” <i>Regular and Chaotic Dynamics</i>, vol. 26, no. 1. Springer Nature, pp. 61–88, 2021.","ama":"Chierchia L, Koudjinan E. V.I. Arnold’s “‘Global’” KAM theorem and geometric measure estimates. <i>Regular and Chaotic Dynamics</i>. 2021;26(1):61-88. doi:<a href=\"https://doi.org/10.1134/S1560354721010044\">10.1134/S1560354721010044</a>","chicago":"Chierchia, Luigi, and Edmond Koudjinan. “V.I. Arnold’s ‘“Global”’ KAM Theorem and Geometric Measure Estimates.” <i>Regular and Chaotic Dynamics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1134/S1560354721010044\">https://doi.org/10.1134/S1560354721010044</a>.","mla":"Chierchia, Luigi, and Edmond Koudjinan. “V.I. Arnold’s ‘“Global”’ KAM Theorem and Geometric Measure Estimates.” <i>Regular and Chaotic Dynamics</i>, vol. 26, no. 1, Springer Nature, 2021, pp. 61–88, doi:<a href=\"https://doi.org/10.1134/S1560354721010044\">10.1134/S1560354721010044</a>.","short":"L. Chierchia, E. Koudjinan, Regular and Chaotic Dynamics 26 (2021) 61–88.","apa":"Chierchia, L., &#38; Koudjinan, E. (2021). V.I. Arnold’s “‘Global’” KAM theorem and geometric measure estimates. <i>Regular and Chaotic Dynamics</i>. Springer Nature. <a href=\"https://doi.org/10.1134/S1560354721010044\">https://doi.org/10.1134/S1560354721010044</a>","ista":"Chierchia L, Koudjinan E. 2021. V.I. Arnold’s ‘“Global”’ KAM theorem and geometric measure estimates. Regular and Chaotic Dynamics. 26(1), 61–88."},"article_type":"original","ddc":["515"],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2010.13243"}],"month":"02","date_published":"2021-02-03T00:00:00Z","date_created":"2020-10-21T14:56:47Z","external_id":{"arxiv":["2010.13243"],"isi":["000614454700004"]},"language":[{"iso":"eng"}],"issue":"1","status":"public","oa_version":"Preprint","doi":"10.1134/S1560354721010044","quality_controlled":"1","publication_identifier":{"issn":["1560-3547"]},"publication":"Regular and Chaotic Dynamics","author":[{"last_name":"Chierchia","first_name":"Luigi","full_name":"Chierchia, Luigi"},{"last_name":"Koudjinan","full_name":"Koudjinan, Edmond","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","first_name":"Edmond","orcid":"0000-0003-2640-4049"}],"year":"2021","date_updated":"2023-08-07T13:37:27Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"V.I. Arnold's ''Global'' KAM theorem and geometric measure estimates","_id":"8689","arxiv":1,"type":"journal_article","volume":26,"isi":1},{"file_date_updated":"2021-05-30T13:57:37Z","publication_status":"submitted","OA_place":"repository","department":[{"_id":"VaKa"}],"article_processing_charge":"No","article_number":"2107.03499","citation":{"apa":"Kaloshin, V., &#38; Koudjinan, E. (n.d.). Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2107.03499\">https://doi.org/10.48550/arXiv.2107.03499</a>","ista":"Kaloshin V, Koudjinan E. Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles. arXiv, 2107.03499.","short":"V. Kaloshin, E. Koudjinan, ArXiv (n.d.).","ieee":"V. Kaloshin and E. Koudjinan, “Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles,” <i>arXiv</i>. .","chicago":"Kaloshin, Vadim, and Edmond Koudjinan. “Non Co-Preservation of the 1/2 and  1/(2l+1)-Rational Caustics along Deformations of Circles.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2107.03499\">https://doi.org/10.48550/arXiv.2107.03499</a>.","ama":"Kaloshin V, Koudjinan E. Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2107.03499\">10.48550/arXiv.2107.03499</a>","mla":"Kaloshin, Vadim, and Edmond Koudjinan. “Non Co-Preservation of the 1/2 and  1/(2l+1)-Rational Caustics along Deformations of Circles.” <i>ArXiv</i>, 2107.03499, doi:<a href=\"https://doi.org/10.48550/arXiv.2107.03499\">10.48550/arXiv.2107.03499</a>."},"abstract":[{"text":"For any given positive integer l, we prove that every plane deformation of a circlewhich preserves the 1/2and 1/ (2l + 1) -rational caustics is trivial i.e. the deformationconsists only of similarities (rescalings and isometries).","lang":"eng"}],"ddc":["500"],"day":"07","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2107.03499","open_access":"1"}],"month":"07","oa":1,"external_id":{"arxiv":["2107.03499"]},"date_published":"2021-07-07T00:00:00Z","file":[{"date_created":"2021-05-30T13:57:37Z","file_size":353431,"file_name":"CoExistence 2&3 caustics 3_17_6_2_3.pdf","creator":"ekoudjin","relation":"main_file","checksum":"b281b5c2e3e90de0646c3eafcb2c6c25","content_type":"application/pdf","access_level":"open_access","date_updated":"2021-05-30T13:57:37Z","file_id":"9436"}],"date_created":"2021-05-30T13:58:13Z","author":[{"first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628"},{"orcid":"0000-0003-2640-4049","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","full_name":"Koudjinan, Edmond","last_name":"Koudjinan","first_name":"Edmond"}],"publication":"arXiv","year":"2021","date_updated":"2025-01-22T08:09:40Z","status":"public","language":[{"iso":"eng"}],"doi":"10.48550/arXiv.2107.03499","oa_version":"Submitted Version","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","_id":"9435","title":"Non co-preservation of the 1/2 and  1/(2l+1)-rational caustics along deformations of circles","type":"preprint","arxiv":1}]