Convergence of KAM iterations for counterterm problems

✍ Scribed by M. Govin; H.R. Jauslin; M. Cibils

• Book ID: 104363753
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 516 KB
• Volume: 9
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(97)00116-1

✦ Synopsis

We analyse two iterative KAM methods for counterterm problems for finite-dimensional matrices. The starting point for these methods is the KAM iteration for Hamiltonians linear in the action variable in classical mechanics. We compare their convergence properties when a perturbation parameter is varied. The first method has no fixed points beyond a critical value of the perturbation parameter. The second one has fixed points for arbitrarily large perturbations. We observe different domains of attraction separated by Julia sets.