Around the stability of KAM tori

DOI10.1215/00127094-3120060zbMath1366.37126arXiv1311.7334OpenAlexW3099004151MaRDI QIDQ2354907

Raphaël Krikorian, Bassam Fayad, L. Hakan Eliasson

Publication date: 27 July 2015

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.7334

zbMATH Keywords

Birkhoff normal formHamiltonian systemKAM tori

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (24)

Lyapunov unstable elliptic equilibria ⋮ General KAM theorems and their applications to invariant tori with prescribed frequencies ⋮ A-posteriori KAM theory with optimal estimates for partially integrable systems ⋮ On the divergence of Birkhoff normal forms ⋮ Hamiltonian and reversible systems with smooth families of invariant tori ⋮ A normal form à la Moser for diffeomorphisms and a generalization of Rüssmann's translated curve theorem to higher dimensions ⋮ Rigorous computer-assisted application of KAM theory: a modern approach ⋮ Attractive invariant circles à la Chenciner ⋮ Positive measure of effective quasi-periodic motion near a Diophantine torus ⋮ Nonlinear stability of elliptic equilibria in Hamiltonian systems with resonances of order four with interactions ⋮ On the fragility of periodic tori for families of symplectic twist maps ⋮ On the optimal effective stability bounds for quasi-periodic tori of finitely differentiable and Gevrey Hamiltonians ⋮ Isolated elliptic fixed points for smooth Hamiltonians ⋮ Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems ⋮ Uniqueness properties of the KAM curve ⋮ Superexponential stability of quasi-periodic motion in Hamiltonian systems ⋮ Non-degenerate Liouville tori are KAM stable ⋮ Effective bounds for the measure of rotations ⋮ Persistence of Lagrange invariant tori at tangent degeneracy ⋮ Super-exponential stability for generic real-analytic elliptic equilibrium points ⋮ Instabilities of invariant quasi-periodic tori ⋮ Persistence of lower dimensional degenerate invariant tori with prescribed frequencies in Hamiltonian systems with small parameter ⋮ Topological weak mixing and diffusion at all times for a class of Hamiltonian systems ⋮ Convergence of the Birkhoff normal form sometimes implies convergence of a normalizing transformation

Cites Work

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