Hamiltonian control of magnetic field lines: computer assisted results proving the existence of KAM barriers

DOI10.3934/jcd.2022002OpenAlexW3122097300WikidataQ114022582 ScholiaQ114022582MaRDI QIDQ2093487

Lorenzo Valvo, Ugo Locatelli

Publication date: 8 November 2022

Published in: Journal of Computational Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2101.07785

zbMATH Keywords

Hamiltonian systemsKAM theorycomputer-assisted proofsnormal form methodscontrolled magnetic fields

Mathematics Subject Classification ID

Three-body problems (70F07) Dynamical systems in control (37N35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Simulation of dynamical systems (37M05) Dynamical systems in classical and celestial mechanics (37N05) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (2)

Existence proof of librational invariant tori in an averaged model of HD60532 planetary system ⋮ Computer-assisted proofs of existence of KAM tori in planetary dynamical models of \(\upsilon\)-And \(\mathbf{b}\)

Cites Work

• Unnamed Item
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• Kolmogorov's normal form for equations of motion with dissipative effects
• Kolmogorov theorem and classical perturbation theory
• Superexponential stability of KAM tori.
• Rigorous computer-assisted application of KAM theory: a modern approach
• Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability in the light of Kolmogorov and Nekhoroshev theories
• Control of chaos in Hamiltonian systems
• Numerical investigations of the structure around an invariant KAM torus using the frequency map analysis
• Computer-assisted estimates for Birkhoff normal forms
• Construction of mappings for Hamiltonian systems and their applications.
• Kolmogorov and Nekhoroshev theory for the problem of three bodies
• Transition from order to chaos, and density limit, in magnetized plasmas
• Perturbation theory and control in classical or quantum mechanics by an inversion formula
• Locally most robust circles and boundary circles for area-preserving maps
• Localized control for non-resonant Hamiltonian systems
• Improved estimates on the existence of invariant tori for Hamiltonian systems
• On the construction of the Kolmogorov normal form for the Trojan asteroids
• Invariant tori in the secular motions of the three-body planetary systems

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