Renormalized Lie perturbation theory
A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another.
- Research Organization:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- DOE Contract Number:
- AM02-76CH03073
- OSTI ID:
- 6378350
- Report Number(s):
- PPPL-1802; ON: DE81025899; TRN: 81-012973
- Country of Publication:
- United States
- Language:
- English
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