Positive measure of KAM tori for finitely differentiable Hamiltonians

DOI10.5802/JEP.137zbMath1473.37074arXiv1812.03067OpenAlexW2905555408WikidataQ114013364 ScholiaQ114013364MaRDI QIDQ2209518

Abed Bounemoura

Publication date: 2 November 2020

Published in: Journal de l'École Polytechnique -- Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.03067

zbMATH Keywords

Hamiltonian systemsKAM theory

Mathematics Subject Classification ID

Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Periodic and quasi-periodic flows and diffeomorphisms (37C55)

Related Items (1)

A KAM theorem for finitely differentiable Hamiltonian systems

Cites Work

• On the existence of invariant tori in nearly-integrable Hamiltonian systems with finitely differentiable perturbations
• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• Destruction of Lagrangian torus for positive definite Hamiltonian systems
• A lecture on the classical KAM theorem
• KAM, α-Gevrey regularity and the α-Bruno-Rüssmann condition
• Integrability of hamiltonian systems on cantor sets
• Generalized implicit function theorems with applications to some small divisor problems, I
• THE EXISTENCE OF CAUSTICS FOR A BILLIARD PROBLEM IN A CONVEX DOMAIN
• KAM theorem for Gevrey Hamiltonians
• 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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