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arXiv · 1908.02523

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

Luigi Chierchia·Comlan Edmond Koudjinan
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Abstract

We review V.I. Arnold's 1963 celebrated paper \cite{ARV63} {\sl Proof of A.N. Kolmogorov's theorem on the conservation of conditionally periodic motions with a small variation in the Hamiltonian}, and prove that, optimizing 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.

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Luigi Chierchia, Comlan Edmond Koudjinan. 2019-08-07. V.I. Arnold's "pointwise" KAM Theorem. https://doi.org/10.1134/s1560354719060017

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