Periodic orbits of the generalized Friedmann-Robertson-Walker Hamiltonian systems

Jaume Llibre; Ammar Makhlouf

doi:10.1007/s10509-012-1314-0

Periodic orbits of the generalized Friedmann-Robertson-Walker Hamiltonian systems

Jaume Llibre, Ammar Makhlouf

Department of Mathematics

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

10 Citations (Scopus)

Abstract

The averaging theory of first order is applied to study a generalization of the Friedmann-Robertson-Walker Hamiltonian systems with three parameters. We provide sufficient conditions on the three parameters of the generalized system to guarantee the existence of continuous families of periodic orbits parameterized by the energy, and these families are given up to first order in a small parameter. © 2012 Springer Science+Business Media Dordrecht.

Original language	English
Pages (from-to)	45-50
Journal	Astrophysics and Space Science
Volume	344
Issue number	1
DOIs	https://doi.org/10.1007/s10509-012-1314-0
Publication status	Published - 1 Jan 2013

Keywords

Averaging theory
Friedmann-Robertson-Walker Hamiltonian system
Periodic orbit

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abstract = "The averaging theory of first order is applied to study a generalization of the Friedmann-Robertson-Walker Hamiltonian systems with three parameters. We provide sufficient conditions on the three parameters of the generalized system to guarantee the existence of continuous families of periodic orbits parameterized by the energy, and these families are given up to first order in a small parameter. {\textcopyright} 2012 Springer Science+Business Media Dordrecht.",

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AU - Makhlouf, Ammar

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N2 - The averaging theory of first order is applied to study a generalization of the Friedmann-Robertson-Walker Hamiltonian systems with three parameters. We provide sufficient conditions on the three parameters of the generalized system to guarantee the existence of continuous families of periodic orbits parameterized by the energy, and these families are given up to first order in a small parameter. © 2012 Springer Science+Business Media Dordrecht.

AB - The averaging theory of first order is applied to study a generalization of the Friedmann-Robertson-Walker Hamiltonian systems with three parameters. We provide sufficient conditions on the three parameters of the generalized system to guarantee the existence of continuous families of periodic orbits parameterized by the energy, and these families are given up to first order in a small parameter. © 2012 Springer Science+Business Media Dordrecht.

KW - Averaging theory

KW - Friedmann-Robertson-Walker Hamiltonian system

KW - Periodic orbit

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DO - 10.1007/s10509-012-1314-0

M3 - Article

VL - 344

SP - 45

EP - 50

JO - Astrophysics and Space Science

JF - Astrophysics and Space Science

SN - 0004-640X

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