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

Jaume Llibre; Pengfei Yuan

doi:https://doi.org/10.1007/s12346-019-00322-y

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

Jaume Llibre, Pengfei Yuan

Department of Mathematics

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3 Citations (Scopus)

Abstract

© 2019, Springer Nature Switzerland AG. 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∈ (0 , 1) a unique elliptic periodic solution with eccentricity e of the Kepler problem can be continued to the mentioned three problems.

Original language	English
Journal	Qualitative Theory of Dynamical Systems
DOIs	https://doi.org/10.1007/s12346-019-00322-y
Publication status	Published - 1 Jan 2019

Keywords

Anisotropic Manev problem
Averaging theory
Hydrogen atom problem
Periodic solutions

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https://doi.org/10.1007/s12346-019-00322-y

https://ddd.uab.cat/record/221304

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title = "Periodic Orbits of the Planar Anisotropic Manev Problem and of the Perturbed Hydrogen Atom Problem",

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keywords = "Anisotropic Manev problem, Averaging theory, Hydrogen atom problem, Periodic solutions",

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AU - Yuan, Pengfei

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N2 - © 2019, Springer Nature Switzerland AG. 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∈ (0 , 1) a unique elliptic periodic solution with eccentricity e of the Kepler problem can be continued to the mentioned three problems.

AB - © 2019, Springer Nature Switzerland AG. 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∈ (0 , 1) a unique elliptic periodic solution with eccentricity e of the Kepler problem can be continued to the mentioned three problems.

KW - Anisotropic Manev problem

KW - Averaging theory

KW - Hydrogen atom problem

KW - Periodic solutions

U2 - https://doi.org/10.1007/s12346-019-00322-y

DO - https://doi.org/10.1007/s12346-019-00322-y

M3 - Article

SN - 1575-5460

JO - Qualitative Theory of Dynamical Systems

JF - Qualitative Theory of Dynamical Systems

ER -

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

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Keywords

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