On the Centre Manifold of Collinear Points in the Planar Three-Body Problem

Details On the Centre Manifold of Collinear Points in the Planar Three-Body Problem On the Centre Manifold of Collinear Points in the Planar Three-Body Problem

Apr 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003cemda..85..311m&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 85, Issue 4, p. 311-340 (2003).

Astronomy and Astrophysics

Astronomy

Three-Body Problem, Libration Points, Homographic Solutions, Kam Theory

Scientific paper

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.

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