V. I. Arnold’s “pointwise” KAM theorem
Chierchia L, Koudjinan E. 2019. V. I. Arnold’s “pointwise” KAM theorem. Regular and Chaotic Dynamics. 24, 583–606.
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Author
Chierchia, Luigi;
Koudjinan, EdmondISTA 
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.
Publishing Year
Date Published
2019-12-10
Journal Title
Regular and Chaotic Dynamics
Volume
24
Page
583–606
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Cite this
Chierchia L, Koudjinan E. V. I. Arnold’s “pointwise” KAM theorem. Regular and Chaotic Dynamics. 2019;24:583–606. doi:10.1134/S1560354719060017
Chierchia, L., & Koudjinan, E. (2019). V. I. Arnold’s “pointwise” KAM theorem. Regular and Chaotic Dynamics. Springer. https://doi.org/10.1134/S1560354719060017
Chierchia, Luigi, and Edmond Koudjinan. “V. I. Arnold’s ‘Pointwise’ KAM Theorem.” Regular and Chaotic Dynamics. Springer, 2019. https://doi.org/10.1134/S1560354719060017.
L. Chierchia and E. Koudjinan, “V. I. Arnold’s ‘pointwise’ KAM theorem,” Regular and Chaotic Dynamics, vol. 24. Springer, pp. 583–606, 2019.
Chierchia L, Koudjinan E. 2019. V. I. Arnold’s “pointwise” KAM theorem. Regular and Chaotic Dynamics. 24, 583–606.
Chierchia, Luigi, and Edmond Koudjinan. “V. I. Arnold’s ‘Pointwise’ KAM Theorem.” Regular and Chaotic Dynamics, vol. 24, Springer, 2019, pp. 583–606, doi:10.1134/S1560354719060017.
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