scientific article; zbMATH DE number 2100980

zbMath1121.37045MaRDI QIDQ4817699

Mikhail B. Sevryuk

Publication date: 15 September 2004

Full work available at URL: http://www.ams.org/distribution/mmj/vol3-3-2003/sevryuk.pdf

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zbMATH Keywords

quasi-periodic motionsHamiltonian systemsKAM theoryinvariant tori

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Differential forms in global analysis (58A10) Nearly integrable Hamiltonian systems, KAM theory (70H08)

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Generic perturbations of linear integrable Hamiltonian systems ⋮ Near-invariant tori on exponentially long time for Poisson systems ⋮ Nekhoroshev's estimates for quasi-periodic time-dependent perturbations ⋮ Partial preservation of frequencies and Floquet exponents in KAM theory ⋮ Gevrey-smoothness of elliptic lower-dimensional invariant tori in Hamiltonian systems under Rüssmann's non-degeneracy condition ⋮ Hamiltonian and reversible systems with smooth families of invariant tori ⋮ Quasi-periodic motions on symplectic tori ⋮ Optimal stability and instability for near-linear Hamiltonians ⋮ Families of invariant tori in KAM theory: interplay of integer characteristics ⋮ Quasi-periodic perturbations within the reversible context 2 in KAM theory ⋮ Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems ⋮ Existence of 3-dimensional tori for 1D complex Ginzburg-Landau equation via a degenerate KAM theorem ⋮ A proof of the invariant torus theorem of Kolmogorov ⋮ Non-degenerate Liouville tori are KAM stable ⋮ Super-exponential stability for generic real-analytic elliptic equilibrium points ⋮ On the Destruction of Resonant Lagrangean Tori in Hamiltonian Systems ⋮ Quasi-effective stability for a nearly integrable volume-preserving mapping

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