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arXiv · 2209.07457

Perturbation theory and canonical coordinates in celestial mechanics

Gabriella Pinzari
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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 V.I.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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Gabriella Pinzari. 2022-09-15. Perturbation theory and canonical coordinates in celestial mechanics. https://doi.org/10.1142/s0129055x24300061

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