Periodic Orbits of the Planar Anisotropic Kepler Problem

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

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8 Citations (Scopus)

Abstract

© 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
Volume27
Issue number3
DOIs
Publication statusPublished - 1 Mar 2017

Keywords

  • Anisotropic Kepler problem
  • averaging theory
  • periodic orbits

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    Abouelmagd, E. I., Llibre, J., & Guirao, J. L. G. (2017). Periodic Orbits of the Planar Anisotropic Kepler Problem. International Journal of Bifurcation and Chaos, 27(3), [1750039]. https://doi.org/10.1142/S0218127417500390