[{"day":"03","page":"61-88","oa_version":"Preprint","publication_status":"published","abstract":[{"lang":"eng","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."}],"date_updated":"2023-08-07T13:37:27Z","status":"public","main_file_link":[{"url":"https://arxiv.org/abs/2010.13243","open_access":"1"}],"publication":"Regular and Chaotic Dynamics","title":"V.I. Arnold's ''Global'' KAM theorem and geometric measure estimates","external_id":{"arxiv":["2010.13243"],"isi":["000614454700004"]},"citation":{"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>","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>.","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.","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>.","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."},"arxiv":1,"scopus_import":"1","issue":"1","author":[{"last_name":"Chierchia","first_name":"Luigi","full_name":"Chierchia, Luigi"},{"full_name":"Koudjinan, Edmond","first_name":"Edmond","last_name":"Koudjinan","id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","orcid":"0000-0003-2640-4049"}],"_id":"8689","oa":1,"date_published":"2021-02-03T00:00:00Z","doi":"10.1134/S1560354721010044","language":[{"iso":"eng"}],"year":"2021","publisher":"Springer Nature","type":"journal_article","month":"02","publication_identifier":{"issn":["1560-3547"]},"quality_controlled":"1","isi":1,"volume":26,"article_type":"original","date_created":"2020-10-21T14:56:47Z","department":[{"_id":"VaKa"}],"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["515"],"intvolume":"        26","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."]}]