Degenerate elliptic resonances

DOI10.1007/s00220-005-1325-6zbMath1080.37063arXivmath/0405420OpenAlexW2007063084MaRDI QIDQ2575360

Giovanni Gallavotti, Guido Gentile

Publication date: 9 December 2005

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0405420

zbMATH Keywords

perturbationsinvariant toriintegrable systemquasiperiodic motionsresummation algorithm

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

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Cites Work

• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
• On elliptic lower dimensional tori in Hamiltonian systems
• Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations
• Perturbations of lower dimensional tori for Hamiltonian systems
• The surviving of lower dimensional tori from a resonant torus of Hamiltonian systems
• Lower dimensional invariant tori in the regions of instability for nearly integrable Hamiltonian systems
• Nearly integrable infinite-dimensional Hamiltonian systems
• Twistless KAM tori
• On Melnikov's persistency problem
• Quasi-periodic solutions for two-level systems
• Lower-dimensional tori for generic Hamiltonian systems
• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• Persistence of lower-dimensional tori under the first Melnikov's non-resonance condition
• Periodic solutions for completely resonant nonlinear wave equations with Dirichlet boundary conditions
• Hyperbolic low-dimensional invariant tori and summations of divergent series
• Construction of periodic solutions of nonlinear wave equations with Dirichlet boundary conditions by the Lindstedt series method
• Construction of periodic solutions of nonlinear wave equations in higher dimension
• Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation
• Birkhoff-Kolmogorov-Arnold-Moser tori in convex Hamiltonian systems
• Quasi-periodic solutions for a nonlinear wave equation
• Convergent series expansions for quasi-periodic motions
• Newton's method and periodic solutions of nonlinear wave equations
• TWISTLESS KAM TORI, QUASI FLAT HOMOCLINIC INTERSECTIONS, AND OTHER CANCELLATIONS IN THE PERTURBATION SERIES OF CERTAIN COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS: A REVIEW
• LINDSTEDT SERIES FOR PERTURBATIONS OF ISOCHRONOUS SYSTEMS: A REVIEW OF THE GENERAL THEORY
• ON FORMAL QUASI-PERIODIC SOLUTIONS OF THE SCHRÖDINGER EQUATION FOR A TWO-LEVEL SYSTEM WITH A HAMILTONIAN DEPENDING QUASI–PERIODICALLY ON TIME
• METHODS FOR THE ANALYSIS OF THE LINDSTEDT SERIES FOR KAM TORI AND RENORMALIZABILITY IN CLASSICAL MECHANICS: A review with Some Applications
• Pointwise convergence of Fourier series
• Renormalization group in statistical mechanics and mechanics: gauge symmetries and vanishing beta functions
• Renormalization group and the Melnikov problem for PDE's
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