@article{8689,
  abstract     = {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.},
  author       = {Chierchia, Luigi and Koudjinan, Edmond},
  issn         = {1560-3547},
  journal      = {Regular and Chaotic Dynamics},
  keywords     = {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.},
  number       = {1},
  pages        = {61--88},
  publisher    = {Springer Nature},
  title        = {{V.I. Arnold's ''Global'' KAM theorem and geometric measure estimates}},
  doi          = {10.1134/S1560354721010044},
  volume       = {26},
  year         = {2021},
}