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Periodic Orbits of the Planar Anisotropic Kepler Problem
Journal article   Peer reviewed

Periodic Orbits of the Planar Anisotropic Kepler Problem

Elbaz I. Abouelmagd, Jaume Llibre and Juan Luis Garcia Guirao
International journal of bifurcation and chaos in applied sciences and engineering, Vol.27(3), p.1750039
03/2017
DOI: https://doi.org/10.1142/S0218127417500390

Abstract

Mathematics Mathematics, Interdisciplinary Applications Multidisciplinary Sciences Physical Sciences Science & Technology Science & Technology - Other Topics
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.

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