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Periodic orbits of perturbed elliptic oscillators in 6D via averaging theory

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Abstract

We provide sufficient conditions on the energy levels to guarantee the existence of periodic orbits for the perturbed elliptic oscillators in 6D using the averaging theory. We give also an analytical estimation of the shape of these periodic orbits parameterized by the energy. The Hamiltonian system here studied comes either from the analysis of the galactic dynamics, or from the motion of the atomic particles in physics.

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Acknowledgements

The second author is partially supported by a MINECO grant MTM2013-40998-P, an AGAUR grant number 2014SGR-568, and the grants FP7-PEOPLE-2012-IRSES 318999 and 316338.

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Authors and Affiliations

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

    Fatima Ezzahra Lembarki & Jaume Llibre

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  1. Fatima Ezzahra Lembarki
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  2. Jaume Llibre
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Correspondence to Jaume Llibre.

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Lembarki, F.E., Llibre, J. Periodic orbits of perturbed elliptic oscillators in 6D via averaging theory. Astrophys Space Sci 361, 340 (2016). https://doi.org/10.1007/s10509-016-2930-x

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  • DOI: https://doi.org/10.1007/s10509-016-2930-x

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