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

@article{Valvo2022HamiltonianCO,
  title={Hamiltonian control of magnetic field lines: Computer assisted results proving the existence of KAM barriers},
  author={L. Sorriso Valvo and Ugo Locatelli},
  journal={Journal of Computational Dynamics},
  year={2022}
}
We reconsider a control theory for Hamiltonian systems, that was introduced on the basis of KAM theory and applied to a model of magnetic field in previous articles. By a combination of Frequency Analysis and of a rigorous (Computer Assisted) KAM algorithm we prove that in the phase space of the magnetic field, due to the control term, a set of invariant tori appear, and it acts as a transport barrier. Our analysis, which is common (but often also limited) to Celestial Mechanics, is based on a… 

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