Kolmogorov and Nekhoroshev theory for the problem of three bodies

Details Kolmogorov and Nekhoroshev theory for the problem of three bodies Kolmogorov and Nekhoroshev theory for the problem of three bodies

Jun 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cemda.104..159g&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 104, Issue 1-2, pp. 159-173

Astronomy and Astrophysics

Astronomy

4

Perturbation Theory, Kam Theory, Nekhoroshev Theory, Exponential Stability, Kolmogorov Theorem, Sun-Jupiter-Saturn System

Scientific paper

We investigate the long time stability in Nekhoroshev’s sense for the Sun- Jupiter-Saturn problem in the framework of the problem of three bodies. Using computer algebra in order to perform huge perturbation expansions we show that the stability for a time comparable with the age of the universe is actually reached, but with some strong truncations on the perturbation expansion of the Hamiltonian at some stage. An improvement of such results is currently under investigation.

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