Periodic Orbits of the Planar Anisotropic Kepler Problem

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

doi:https://doi.org/10.1142/S0218127417500390

Periodic Orbits of the Planar Anisotropic Kepler Problem

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

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

21 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 language	English
Article number	1750039
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	27
Issue number	3
DOIs	https://doi.org/10.1142/S0218127417500390
Publication status	Published - 1 Mar 2017

Keywords

Anisotropic Kepler problem
averaging theory
periodic orbits

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https://doi.org/10.1142/S0218127417500390

https://ddd.uab.cat/record/182514

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title = "Periodic Orbits of the Planar Anisotropic Kepler Problem",

abstract = "{\textcopyright} 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.",

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Y1 - 2017/3/1

N2 - © 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.

AB - © 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.

KW - Anisotropic Kepler problem

KW - averaging theory

KW - periodic orbits

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M3 - Article

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IS - 3

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Periodic Orbits of the Planar Anisotropic Kepler Problem

Abstract

Keywords

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