Kolmogorov-Arnold-Moser (KAM) theory for finite and infinite dimensional systems

DOI10.1007/978-1-0716-2621-4_302zbMATH Open1548.37007MaRDI QIDQ6599395

Publication date: 6 September 2024

Singular perturbations in context of PDEs (35B25) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbations in context of PDEs (35B20) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)

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Reducible quasi-periodic solutions for the non linear Schrödinger equation
KAM for the Klein Gordon equation on \(\mathbb {S}^d\)
Planetary Birkhoff normal forms
A KAM algorithm for the resonant non-linear Schrödinger equation
Arnold diffusion. I: Announcement of results
Properly-degenerate KAM theory (following V. I. Arnold)
An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger equation
KAM for the quantum harmonic oscillator
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KAM for the nonlinear beam equation
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The imbedding problem for Riemannian manifolds
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KAM for the nonlinear Schrödinger equation
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Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation
Natural boundaries for area-preserving twist maps
Nearly integrable infinite-dimensional Hamiltonian systems
Second order Hamiltonian equations on \(\mathbb{T}^ \infty\) and almost- periodic solutions
Large scale chaos and marginal stability in the solar system
Invariant tori for nearly integrable Hamiltonian systems with degeneracy
KAM tori for 1D nonlinear wave equations with periodic boundary conditions
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KAM theory in configuration space
Moser's theorem for lower dimensional tori
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KAM-stable Hamiltonians
The defocusing NLS equation and its normal form
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Iteration of analytic functions
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Stable and Random Motions in Dynamical Systems
Non-existence of invariant circles
A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS
Integrability of hamiltonian systems on cantor sets
Rigorous estimates for a computer-assisted KAM theory
PERTURBATION THEORY FOR QUASIPERIODIC SOLUTIONS OF INFINITE-DIMENSIONAL HAMILTONIAN SYSTEMS, AND ITS APPLICATION TO THE KORTEWEG-DE VRIES EQUATION
Generalized implicit function theorems with applications to some small divisor problems, II
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A renormalization group for Hamiltonians, with applications to KAM tori
TWISTLESS KAM TORI, QUASI FLAT HOMOCLINIC INTERSECTIONS, AND OTHER CANCELLATIONS IN THE PERTURBATION SERIES OF CERTAIN COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS: A REVIEW
KAM theory without action-angle variables
Accurate strategies for small divisor problems
On the construction of almost periodic solutions for a nonlinear Schrödinger equation
Démonstration du ‘théorème d'Arnold’ sur la stabilité du système planétaire (d'après Herman)
The KAM Story

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