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- W2764078091 abstract "Arnold showed the existence of quasi-periodic solutions in the plane planetary three-body prob- lem, provided that the mass of two of the bodies, the planets, is small compared to the mass of the third one, the Sun. This smallness condition depends in a sensitive way on the analyticity widths of the Hamiltonian of the three-body problem, expressed with the help of some tran- scendental coordinates. Henon gave a minimal ratio of masses necessary to the application of Arnold’s theorem. The main objective of this thesis is to determine a sufficient condition on this ratio. A first part of this work consists in estimating these analyticity widths, which requires a precise study of the complex Kepler equation, as well as the complex singularities of the disturb- ing function. A second part consists in reworking the Hamiltonian to put it under normal form, in order to apply the KAM theorem (KAM standing for Kolmogorov-Arnold-Moser). In this aim, it is essential to work with the secular Hamiltonian to put it under a suitable normal form. We can then quantify the non-degeneracy of the secular Hamiltonian, as well as estimate the perturbation. Finally, it is necessary to derive a quantitative version of the KAM theorem, in order to identify the hypotheses necessary for its application to the plane three-body problem. After this work, it is shown that the KAM theorem can be applied for a ratio of masses that is close to 10^(−85) between the planets and the star." @default.
- W2764078091 created "2017-10-20" @default.
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- W2764078091 date "2017-04-21" @default.
- W2764078091 modified "2023-10-16" @default.
- W2764078091 title "Stability in the plane planetary three-body problem" @default.
- W2764078091 hasPublicationYear "2017" @default.
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