KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by Arnold in the 60s who worked out a theorem, that he named the “Fundamental Theorem” (FT), especially designed for the planetary problem. However, FT could be really used at that purpose only when, about 50 years later, a set of coordinates constructively taking the invariance by rotation and close-to-integrability into account was used. Since then, some progress has been done in the symplectic assessment of the problem, and here we review such results.
Perturbation theory and canonical coordinates in celestial mechanics
Pinzari G.
Conceptualization
2024
Abstract
KAM theory owes most of its success to its initial motivation: the application to problems of celestial mechanics. The masterly application was offered by Arnold in the 60s who worked out a theorem, that he named the “Fundamental Theorem” (FT), especially designed for the planetary problem. However, FT could be really used at that purpose only when, about 50 years later, a set of coordinates constructively taking the invariance by rotation and close-to-integrability into account was used. Since then, some progress has been done in the symplectic assessment of the problem, and here we review such results.
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