On the existence of invariant tori in nearly-integrable Hamiltonian systems with finitely differentiable perturbations

DOI10.1134/S1560354707030033zbMath1229.70058MaRDI QIDQ655263

Juan-Miguel Gracia

Publication date: 3 January 2012

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

zbMATH Keywords

quasi-periodic motionsperturbationsKAM theoryinvariant toricelestial mechanicssmall divisorsHölder conditionnearly integrable Hamiltonian systemstrigonometric approximation in several variables

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) Celestial mechanics (70F15) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (8)

Periodic perturbations of Hamiltonian systems ⋮ Unnamed Item ⋮ Nekhoroshev estimates for finitely differentiable quasi-convex Hamiltonians ⋮ A KAM theorem for finitely differentiable Hamiltonian systems ⋮ Positive measure of KAM tori for finitely differentiable Hamiltonians ⋮ Orbit determination for standard-like maps: asymptotic expansion of the confidence region in regular zones ⋮ Total destruction of Lagrangian tori ⋮ On the reducibility of a class of finitely differentiable quasi-periodic linear systems

Cites Work

• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• Lectures on celestial mechanics. Transl. from the German by C. I. Kalme.
• Integrability of hamiltonian systems on cantor sets
• Generalized implicit function theorems with applications to some small divisor problems, I
• Generalized implicit function theorems with applications to some small divisor problems, II
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