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