Hamiltonian Control of Magnetic Field Lines: Computer Assisted Results Proving the Existence of KAM Barriers
Abstract
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 normal form approach; it is also quite general and can be applied to quasiintegrable Hamiltonian systems satisfying a few additional mild assumptions. As a novelty with respect to the works that in the last two decades applied Computer Assisted Proofs into the framework of KAM theory, we provide all the codes allowing to produce our results. They are collected in a software package that is publicly available from the {\it Mendeley Data} repository. All these codes are designed in such a way to be easytouse, also for what concerns eventual adaptations for applications to similar problems.
 Publication:

arXiv eprints
 Pub Date:
 January 2021
 arXiv:
 arXiv:2101.07785
 Bibcode:
 2021arXiv210107785V
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematical Physics
 EPrint:
 Version 2