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Periodic Orbits of the Planar Anisotropic Manev Problem and of the Perturbed Hydrogen Atom Problem

  • Jaume LlibreEmail author
  • Pengfei Yuan
Article
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Part of the following topical collections:
  1. In Memoriam Florin Diacu

Abstract

In this paper we use the averaging theory for studying the periodic solutions of the planar anisotropic Manev problem and of two perturbations of the hydrogen atom problem. When a convenient parameter is sufficiently small we prove that for every value \(e\in (0,1)\) a unique elliptic periodic solution with eccentricity e of the Kepler problem can be continued to the mentioned three problems.

Keywords

Periodic solutions Averaging theory Anisotropic Manev problem Hydrogen atom problem 

Notes

Acknowledgements

We thank to the reviewer his/her many comments and suggestions which help us to improve the presentation of our results. The first author is partially supported by the Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación grants MTM2016-77278-P (FEDER) and MDM-2014-0445, the Agència de Gestió d’Ajuts Universitaris i de Recerca Grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911. The second author is partially supported by Fundamental Research Funds for the Central Universities (NO.XDJK2015C139), China Scholarship Council(N0.201708505030).

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Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBarcelonaSpain
  2. 2.School of Mathematics and StatisticsSouthwest UniversityChongqingChina

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