Periodic orbits of the Sitnikov problem via a Poincaré map

Montserrat Corbera, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

31 Citations (Scopus)

Abstract

In this paper by means of a Poincaré map, we prove the existence of symmetric periodic orbits of the elliptic Sitnikov problem. Furthermore, using the presence of the Bernoulli shift as a subsystem of that Poincaré map, we prove that not all the periodic orbits of the Sitnikov problem are symmetric periodic orbits.
Original languageEnglish
Pages (from-to)273-303
JournalCelestial Mechanics and Dynamical Astronomy
Volume77
DOIs
Publication statusPublished - 1 Jan 2000

Keywords

  • Periodic orbits
  • Poincaré map
  • Sitnikov motions
  • Symmetric periodic orbits

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