V.I. Arnold's ''Global'' KAM theorem and geometric measure estimates Chierchia, Luigi Koudjinan, Edmond ; https://orcid.org/0000-0003-2640-4049 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. ddc:515 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. Springer Nature 2021 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/8689 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1134/S1560354721010044 info:eu-repo/semantics/altIdentifier/issn/1560-3547 info:eu-repo/semantics/altIdentifier/wos/000614454700004 info:eu-repo/semantics/altIdentifier/arxiv/2010.13243 info:eu-repo/semantics/openAccess