Chierchia, Luigi; Pinzari, Gabriella Properly-degenerate KAM theory (following V. I. Arnold). (English) Zbl 1282.37033 Discrete Contin. Dyn. Syst., Ser. S 3, No. 4, 545-578 (2010). Summary: V. I. Arnold’s “Fundamental Theorem” on properly-degenerate systems [Russ. Math. Surv. 18, No. 6, 85–191 (1963); translation from Usp. Mat. Nauk 18, No. 6(114), 91–192 (1963), Chapter IV] is revisited and improved with particular attention to the relation between the perturbative parameters and to the measure of the Kolmogorov set. Relations with the planetary many-body problem are shortly discussed. Cited in 14 Documents MSC: 37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion 70F10 \(n\)-body problems 70F15 Celestial mechanics 70H08 Nearly integrable Hamiltonian systems, KAM theory Keywords:KAM theory; Kolmogorov set; many-body problem; small divisors; invariant tori; degeneracies PDFBibTeX XMLCite \textit{L. Chierchia} and \textit{G. Pinzari}, Discrete Contin. Dyn. Syst., Ser. S 3, No. 4, 545--578 (2010; Zbl 1282.37033) Full Text: DOI