KAM tori: persistence and smoothness

DOI10.1088/0951-7715/21/10/T01zbMath1148.37032MaRDI QIDQ3531231

Mikhail B. Sevryuk

Publication date: 21 October 2008

Published in: Nonlinearity (Search for Journal in Brave)

zbMATH Keywords

perturbationsinvariant toriFloquet exponentsKolmogorov-Arnold-Moser theorypartially integrable systemspreservation of frequenciesten open problems

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) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Nearly integrable Hamiltonian systems, KAM theory (70H08)

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Whitney smooth families of invariant tori within the reversible context 2 of KAM theory ⋮ Partial preservation of frequencies and Floquet exponents of invariant tori in the reversible KAM context 2 ⋮ Hamiltonian and reversible systems with smooth families of invariant tori ⋮ A Galilean dance 1:2:4 resonant periodic motions and their librations of Jupiter and his Galilean moons ⋮ Tracing KAM tori in presymplectic dynamical systems ⋮ Quasi-periodic solutions of derivative nonlinear Schrödinger equations with a given potential ⋮ The reversible context 2 in KAM theory: the first steps ⋮ Quasi-periodic perturbations within the reversible context 2 in KAM theory ⋮ Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems ⋮ Global structure of regular tori in a generic 4D symplectic map

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