This article is cited in 7 papers

V. I. Arnold's "Pointwise" KAM Theorem

L. Chierchia, C. E. Koudjinan

Dipartimento di Matematica, Università Roma Tre, Largo S. L. Murialdo 1, I-00146 Roma, Italy

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 $\varepsilon \to 0$, $\varepsilon$ being the strength of the perturbation). All constants involved are explicitly computed.

Keywords: Nearly-integrable Hamiltonian systems, KAM theory, Arnold's Theorem, small divisors, perturbation theory, symplectic transformations.

MSC: 37J40, 37J05, 37J25, 70H08

Received: 11.09.2019
Accepted: 11.10.2019

Language: English

DOI: 10.1134/S1560354719060017

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