On the centre manifold of collinear points in the planar three-body problem

Regina Martínez, Anna Samà

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)311-340
JournalCelestial Mechanics and Dynamical Astronomy
Volume85
DOIs
Publication statusPublished - 1 Apr 2003

Keywords

  • Homographic solutions
  • KAM theory
  • Libration points
  • Three-body problem

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