Ejection-collision orbits and invariant punctured tori in a restricted four-body problem

Dante L. Maranhão, Jaume Llibre

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26 Citations (Scopus)


We study the motion of an infinitesimal mass point under the gravitational action of three mass points of masses μ, 1 - 2μ and μ moving under Newton's gravitational law in circular periodic orbits around their center of masses. The three point masses form at any time a collinear central configuration. The body of mass 1 - 2μ is located at the center of mass. The paper has two main goals. First, to prove the existence of four transversal ejection-collision orbits, and second to show the existence of an uncountable number of invariant punctured tori. Both results are for a given large value of the Jacobi constant and for an arbitrary value of the mass parameter 0 < μ ≤ 1/2.
Original languageEnglish
Pages (from-to)1-14
JournalCelestial Mechanics and Dynamical Astronomy
Issue number1
Publication statusPublished - 1 Jan 1998


  • Ejection-collision orbits
  • Invariant tori
  • Restricted problem


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