Abstract
We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically.
Original language | English |
---|---|
Pages (from-to) | 311-340 |
Journal | Celestial Mechanics and Dynamical Astronomy |
Volume | 85 |
DOIs | |
Publication status | Published - 1 Apr 2003 |
Keywords
- Homographic solutions
- KAM theory
- Libration points
- Three-body problem