Periodic orbits for a generalized Friedmann-Robertson-Walker Hamiltonian system in dimension $6$

Fatima Ezzahra  Lembarki; Jaume  Llibre

doi:10.3934/dcdss.2015.8.1165

Article Contents

2015, Volume 8, Issue 6: 1165-1211. Doi: 10.3934/dcdss.2015.8.1165

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Periodic orbits for a generalized Friedmann-Robertson-Walker Hamiltonian system in dimension $6$

Fatima Ezzahra Lembarki^1, and
Jaume Llibre^1,

1.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia

Received: June 30, 2015

Revised: August 31, 2015

Published: November 2015

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Abstract

A generalized Friedmann-Robertson-Walker Hamiltonian system is studied in dimension $6$. The averaging theory is the tool used to provide sufficient conditions on the six parameters of the system which guarantee the existence of continuous families of period orbits parameterized by the energy.

Keywords:

Periodic orbits,
Friedmann-Robertson-Walker,
averaging theory,
family of periodic orbits,
periodic orbits parameterized by the energy.

Mathematics Subject Classification: Primary: 37G15, 37C80, 37C30.

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