Bridges between the Generalized Sitnikov Family and the Lyapunov Family of Periodic Orbits

Jaume Llibre, Kenneth R. Meyer, Jaume Soler

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

The linearization of the spatial restricted three-body problem at the collinear equilibrium point L2has two pairs of pure imaginary eigenvalues and one pair of real eigenvalues so the center manifold is four dimensional. By the classical Lyapunov center theorem there are two families of periodic solutions emanating from this equilibrium point. Using normal form techniques we investigate the existence of bridges of periodic solutions connecting these two Lyapunov families. A bridge is a third family of periodic solutions which bifurcates from both the Lyapunov families. We show that for the mass ratio parameterμnear 1/2 and near 0 there are many bridges of periodic solutions. © 1999 Academic Press.
Original languageEnglish
Pages (from-to)140-156
JournalJournal of Differential Equations
Volume154
DOIs
Publication statusPublished - 1 May 1999

Keywords

  • Hill's lunar problem
  • KAM tori
  • Normal form
  • Periodic solutions
  • Restricted three-body problem

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