{"abstract":[{"text":"Given l>2ν>2d≥4, we prove the persistence of a Cantor--family of KAM tori of measure O(ε1/2−ν/l) for any non--degenerate nearly integrable Hamiltonian system of class Cl(D×Td), where D⊂Rd is a bounded domain, provided that the size ε of the perturbation is sufficiently small. This extends a result by D. Salamon in \\cite{salamon2004kolmogorov} according to which we do have the persistence of a single KAM torus in the same framework. Moreover, it is well--known that, for the persistence of a single torus, the regularity assumption can not be improved.","lang":"eng"}],"keyword":["Analysis"],"day":"05","main_file_link":[{"url":"https://arxiv.org/abs/1909.04099","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","publisher":"Elsevier","intvolume":"       269","title":"A KAM theorem for finitely differentiable Hamiltonian systems","oa":1,"quality_controlled":"1","article_type":"original","doi":"10.1016/j.jde.2020.03.044","citation":{"short":"E. Koudjinan, Journal of Differential Equations 269 (2020) 4720–4750.","mla":"Koudjinan, Edmond. “A KAM Theorem for Finitely Differentiable Hamiltonian Systems.” <i>Journal of Differential Equations</i>, vol. 269, no. 6, Elsevier, 2020, pp. 4720–50, doi:<a href=\"https://doi.org/10.1016/j.jde.2020.03.044\">10.1016/j.jde.2020.03.044</a>.","ista":"Koudjinan E. 2020. A KAM theorem for finitely differentiable Hamiltonian systems. Journal of Differential Equations. 269(6), 4720–4750.","chicago":"Koudjinan, Edmond. “A KAM Theorem for Finitely Differentiable Hamiltonian Systems.” <i>Journal of Differential Equations</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jde.2020.03.044\">https://doi.org/10.1016/j.jde.2020.03.044</a>.","ama":"Koudjinan E. A KAM theorem for finitely differentiable Hamiltonian systems. <i>Journal of Differential Equations</i>. 2020;269(6):4720-4750. doi:<a href=\"https://doi.org/10.1016/j.jde.2020.03.044\">10.1016/j.jde.2020.03.044</a>","ieee":"E. Koudjinan, “A KAM theorem for finitely differentiable Hamiltonian systems,” <i>Journal of Differential Equations</i>, vol. 269, no. 6. Elsevier, pp. 4720–4750, 2020.","apa":"Koudjinan, E. (2020). A KAM theorem for finitely differentiable Hamiltonian systems. <i>Journal of Differential Equations</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jde.2020.03.044\">https://doi.org/10.1016/j.jde.2020.03.044</a>"},"article_processing_charge":"No","external_id":{"arxiv":["1909.04099"]},"date_published":"2020-09-05T00:00:00Z","status":"public","_id":"8691","page":"4720-4750","extern":"1","publication":"Journal of Differential Equations","author":[{"id":"52DF3E68-AEFA-11EA-95A4-124A3DDC885E","orcid":"0000-0003-2640-4049","first_name":"Edmond","full_name":"Koudjinan, Edmond","last_name":"Koudjinan"}],"date_updated":"2021-01-12T08:20:33Z","date_created":"2020-10-21T15:03:05Z","issue":"6","language":[{"iso":"eng"}],"year":"2020","publication_identifier":{"issn":["0022-0396"]},"volume":269,"oa_version":"Preprint","month":"09","publication_status":"published"}