V. I. Arnold's ``Pointwise KAM theorem

DOI10.1134/S1560354719060017zbMath1435.37085arXiv1908.02523MaRDI QIDQ2297600

Comlan E. Koudjinan, Luigi Chierchia

Publication date: 20 February 2020

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.02523

zbMATH Keywords

perturbation theoryKAM theoryArnold's theoremsmall divisorssymplectic transformationsnearly-integrable Hamiltonian systems

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Nearly integrable Hamiltonian systems, KAM theory (70H08) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06)

Related Items (3)

The relation between the size of perturbations and the dimension of tori in an infinite-dimensional KAM theorem of Pöschel ⋮ A KAM theorem for finitely differentiable Hamiltonian systems ⋮ V. I. Arnold's ``Global KAM theorem and geometric measure estimates

Cites Work

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• Kolmogorov's 1954 paper on nearly-integrable Hamiltonian systems
• Explicit estimates on the measure of primary KAM tori
• Kolmogorov theorem revisited
• Estimates in the Kolmogorov theorem on conservation of conditionally periodic motions
• Effective stability and KAM theory
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• Integrability of hamiltonian systems on cantor sets
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN

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