Periodic Orbits of the Planar Anisotropic Kepler Problem

Elbaz I. Abouelmagd, Jaume Llibre, Juan Luis García Guirao

Research output: Contribution to journalArticleResearchpeer-review

21 Citations (Scopus)


© 2017 World Scientific Publishing Company. In this paper, we prove that at every energy level the anisotropic Kepler problem with small anisotropy has two periodic orbits which bifurcate from elliptic orbits of the Kepler problem with high eccentricity. Moreover we provide approximate analytic expressions for these periodic orbits. The tool for proving this result is the averaging theory.
Original languageEnglish
Article number1750039
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number3
Publication statusPublished - 1 Mar 2017


  • Anisotropic Kepler problem
  • averaging theory
  • periodic orbits


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