The KAM Story
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Publication:5407955
DOI10.1142/8955zbMath1362.37004OpenAlexW4250021600MaRDI QIDQ5407955
Publication date: 8 April 2014
Full work available at URL: https://doi.org/10.1142/8955
History of mathematics in the 20th century (01A60) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory (37-01) Nearly integrable Hamiltonian systems, KAM theory (70H08) History of dynamical systems and ergodic theory (37-03)
Related Items (33)
On emergence and complexity of ergodic decompositions ⋮ Whitney smooth families of invariant tori within the reversible context 2 of KAM theory ⋮ Maximum attainable energy in a fixed-frequency cyclotron ⋮ A-posteriori KAM theory with optimal estimates for partially integrable systems ⋮ Foundations of a finite non-equilibrium statistical thermodynamics: extrinsic quantities ⋮ The Kolmogorov-Arnold-Moser (KAM) and Nekhoroshev Theorems with Arbitrary Time Dependence ⋮ Periodic perturbations of Hamiltonian systems ⋮ Existence of quasiperiodic solutions of elliptic equations on \(\mathbb{R}^{N + 1}\) via center manifold and KAM theorems ⋮ 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 ⋮ Isodrastic magnetic fields for suppressing transitions in guiding-centre motion ⋮ Translation of the V. I. Arnold paper ``From superpositions to KAM theory ⋮ Elliptic Bubbles in Moser's 4D Quadratic Map: The Quadfurcation ⋮ Mini-course: Classical mechanics and transport ⋮ The physics and applications of strongly coupled Coulomb systems (plasmas) levitated in electrodynamic traps ⋮ On the fragility of periodic tori for families of symplectic twist maps ⋮ Families of invariant tori in KAM theory: interplay of integer characteristics ⋮ Measure and Capacity of Wandering Domains in Gevrey Near-integrable Exact Symplectic Systems ⋮ A Window into the World of KAM Theory ⋮ Law without law or ``just limit theorems? Some reflections about a proposal of Wheeler's ⋮ Moser's quadratic, symplectic map ⋮ Periodic Solutions to a Perturbed Relativistic Kepler Problem ⋮ Explicit estimates on the measure of primary KAM tori ⋮ Asymptotic stability estimates near an equilibrium point ⋮ A conceptual approach to the problem of action-angle variables ⋮ Effective bounds for the measure of rotations ⋮ Classical dynamics of harmonically trapped interacting particles ⋮ K for KAM. Kolmogorov-Arnold-Moser. Translated from the Italian ⋮ Quantitative statistical stability and linear response for irrational rotations and diffeomorphisms of the circle ⋮ Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic Dynamics ⋮ The mathematics of asymptotic stability in the Kuramoto model ⋮ KAM for the nonlinear wave equation on the circle: a normal form theorem ⋮ Perturbations of superintegrable systems
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