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RESEARCH PRODUCT
Convergence of KAM iterations for counterterm problems
Hans-rudolf JauslinM. CibilsM. Govinsubject
Arbitrarily largeGeneral MathematicsApplied MathematicsMathematical analysisGeneral Physics and AstronomyPerturbation (astronomy)Statistical and Nonlinear PhysicsFixed pointAction variableCritical valueJulia setMathematicsdescription
Abstract 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1998-03-01 | Chaos, Solitons & Fractals |