On the families of periodic orbits of the sitnikov problem

Jaume Llibre, Rafel Ortega

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28 Citations (Scopus)


The main goal of this paper is to study analytically the families of symmetric periodic orbits of the elliptic Sitnikov problem for all values of the eccentricity in the interval [0,1), providing qualitative and quantitative information on the bifurcation diagram of such families of periodic orbits. The basic tool for proving our results is the global continuation method of the zeros of a function depending on one parameter provided by Leray and Schauder and based in the Brouwer degree. © 2008 Society for Industrial and Applied Mathematics.
Original languageEnglish
Pages (from-to)561-576
JournalSIAM Journal on Applied Dynamical Systems
Issue number2
Publication statusPublished - 11 Dec 2008


  • 3-body problem
  • Global continuation
  • Periodic orbits
  • Sitnikov problem


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