CAP4KAM2D: Computer-Assisted Proofs For demonstrating the existence of 2-Dimensional KAM tori

In the folder you can produce by uncompressing the attached zipped file (namely, that folder is called "CAP4KAM"), you should find everything you need in order to perform a complete computer-assisted proof of existence of invariant tori for a Hamiltonian that satifies three assumptions: (i) it describes a (Hamiltonian) system with two degrees of freedom; (ii) it is close enough to a Kolmogorov normal form (so fulfilling also both the non-resonance and non-degeneracy conditions usually adopted in the framework of KAM theory); (iii) its expansion in Taylor-Fourier series (in its action-angle canonical coordinates) is finite.

The software included in the folder "CAP4KAM" refers to the following paper: [VL] Valvo L., Locatelli U.: "Hamiltonian Control of Magnetic Field Lines: Computer Assisted Results Proving the Existence of KAM Barriers", preprint (2021); available both at the web address arxiv.org/abs/2101.07785 and in a pdf copy you can find in the attachments. That work should not be too difficult to read for people working in the field of Hamiltonian perturbation theory and, in particular, it should clarify the three assumptions listed above.