We review V. I. Arnold’s 1963 celebrated paper [1] Proof of A. N. Kolmogorov’s Theorem on the Conservation of Conditionally Periodic Motions with a Small Variation in the Hamiltonian, and prove that, optimising Arnold’s scheme, one can get “sharp” asymptotic quantitative conditions (as ε → 0, ε being the strength of the perturbation). All constants involved are explicitly computed.
Chierchia, L., Koudjinan, C.E. (2019). V. I. Arnold’s “Pointwise” KAM Theorem. REGULAR & CHAOTIC DYNAMICS, 24(6), 583-606 [10.1134/S1560354719060017].
V. I. Arnold’s “Pointwise” KAM Theorem
Chierchia L.
;
2019-01-01
Abstract
We review V. I. Arnold’s 1963 celebrated paper [1] Proof of A. N. Kolmogorov’s Theorem on the Conservation of Conditionally Periodic Motions with a Small Variation in the Hamiltonian, and prove that, optimising Arnold’s scheme, one can get “sharp” asymptotic quantitative conditions (as ε → 0, ε being the strength of the perturbation). All constants involved are explicitly computed.File in questo prodotto:
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