Abstract:
This paper continues the discussion started in [10] 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 set are provided in 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.
Keywords:
nearly-integrable Hamiltonian systems, perturbation theory, KAM theory, Arnold’s
scheme, Kolmogorov set, primary invariant tori, Lagrangian tori, measure estimates, small
divisors, integrability on nowhere dense sets, Diophantine frequencies.
\Bibitem{ChiKou21}
\by Luigi Chierchia, Comlan E. Koudjinan
\paper V. I.Arnold’s “Global” KAM Theorem and Geometric Measure
Estimates
\jour Regul. Chaotic Dyn.
\yr 2021
\vol 26
\issue 1
\pages 61--88
\mathnet{http://mi.mathnet.ru/rcd1102}
\crossref{https://doi.org/10.1134/S1560354721010044}
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Linking options:
https://www.mathnet.ru/eng/rcd1102
https://www.mathnet.ru/eng/rcd/v26/i1/p61
This publication is cited in the following 3 articles:
Livia Corsi, Guido Gentile, Michela Procesi, “Maximal Tori in Infinite-Dimensional Hamiltonian Systems: a Renormalisation Group Approach”, Regul. Chaotic Dyn., 29:4 (2024), 677–715
Chang Liu, Jiamin Xing, “A NEW PROOF OF MOSER'S THEOREM”, jaac, 12:4 (2022), 1679
A. I. Neishtadt, D. V. Treschev, “Dynamical phenomena connected with stability loss of equilibria and periodic trajectories”, Russian Math. Surveys, 76:5 (2021), 883–926
Citation in format AMSBIB
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